Solved: Find the current through and the potential

What is a circuit?

How are circuits analyzed?

How do circuits use energy?

How are resistors combined?

What is an RC circuit?

Why are circuits important?

Which of these diagrams represent the same circuit?

Analyze the circuit shown in FIGURE 28.8. a. Find the current in and the potential difference across each resistor. b. Draw a graph showing how the potential changes around the circuit, starting from V = 0 V at the negative terminal of the 6 V battery.

What is V across the unspecified circuit element? Does the potential increase or decrease when traveling through this element in the direction assigned to I?

How much current is drawn by a 100 W lightbulb connected to a 120 V outlet?

Most loudspeakers are designed to have a resistance of 8 . If an 8 loudspeaker is connected to a stereo amplifier with a rating of 100 W, what is the maximum possible current to the loudspeaker?

Rank in order, from largest to smallest, the powers Pa to Pd dissipated in resistors a to d.

a. What is the current in the circuit of FIGURE 28.15a? b. Draw a graph of potential versus position in the circuit, going cw from V = 0 V at the batterys negative terminal.

What are the current and the potential at points a to e?

A 6 flashlight bulb is powered by a 3 V battery with an internal resistance of 1 . What are the power dissipation of the bulb and the terminal voltage of the battery?

Rank in order, from brightest to dimmest, the identical bulbs A to D.

What is the short-circuit current of a 12 V car battery with an internal resistance of 0.020 ? What happens to the power supplied by the battery?

The time constant for the discharge of this capacitor is a. 5 s. b. 4 s. c. 2 s. d. 1 s. e. The capacitor doesnt discharge because the resistors cancel each other.

The three resistors of FIGURE 28.22 are connected to a 9 V battery. Find the potential difference across and the current through each resistor.

What is the equivalent resistance of the group of resistors shown in FIGURE 28.24?

Find the current through and the potential difference across each of the four resistors in the circuit shown in FIGURE 28.28.

Find the current through and the potential difference across the 100 resistor in the circuit of FIGURE 28.30.

Suppose the circuit of Figure 28.32 were grounded at the junction between the two resistors instead of at the bottom. Find the potential at each corner of the circuit

To determine the capacitance of an unmarked capacitor, you set up the circuit shown in FIGURE 28.36. After holding the switch in position a for several seconds, you suddenly flip itat t = 0 sto position b while monitoring the resistor voltage with a voltmeter. Your measurements are shown in the table. What is the capacitance? And what was the resistor current 5.0 s after the switch changed position?

The switch in FIGURE 28.39 has been in position a for a long time. It is suddenly switched to position b for 1.0 s, then back to a. How much energy is dissipated by the 5500 resistor?

Rank in order, from largest to smallest, the currents Ia to Id through the four resistors in FIGURE Q28.1.

The tip of a flashlight bulb is touching the top of the 3 V battery in FIGURE Q28.2. Does the bulb light? Why or why not?

The wire is broken on the right side of the circuit in FIGURE Q28.3. What is the potential difference V1 - V2 between points 1 and 2? Explain.

The circuit of FIGURE Q28.4 has two resistors, with R1 7 R2. Which of the two resistors dissipates the larger amount of power? Explain.

The circuit of FIGURE Q28.5 has two resistors, with R1 7 R2. Which of the two resistors dissipates the larger amount of power? Explain

Rank in order, from largest to smallest, the powers Pa to Pd dissipated by the four resistors in FIGURE Q28.6.

Are the two resistors in FIGURE Q28.7 in series or in parallel? Explain.

A battery with internal resistance r is connected to a load resistance R. If R is increased, does the terminal voltage of the battery increase, decrease, or stay the same? Explain.

Initially bulbs A and B in FIGURE Q28.9 are glowing. What happens to each bulb if the switch is closed? Does it get brighter, stay the same, get dimmer, or go out? Explain.

Bulbs A, B, and C in FIGURE Q28.10 are identical, and all are glowing. a. Rank in order, from most to least, the brightnesses of the three bulbs. Explain. b. Suppose a wire is connected between points 1 and 2. What happens to each bulb? Does it get brighter, stay the same, get dimmer, or go out? Explain.

Bulbs A and B in FIGURE Q28.11 are identical, and both are glowing. Bulb B is removed from its socket. Does the potential difference V12 between points 1 and 2 increase, stay the same, decrease, or become zero? Explain.

Bulbs A and B in FIGURE Q28.12 are identical, and both are glowing. What happens to each bulb when the switch is closed? Does its brightness increase, stay the same, decrease, or go out? Explain

FIGURE Q28.13 shows the voltage as a function of time of a capacitor as it is discharged (separately) through three different resistors. Rank in order, from largest to smallest, the values of the resistances R1 to R3.

Draw a circuit diagram for the circuit of FIGURE EX28.1.

Draw a circuit diagram for the circuit of FIGURE EX28.2.

In FIGURE EX28.3, what is the magnitude of the current in the wire to the right of the junction? Does the charge in this wire flow to the right or to the left?

a. What are the magnitude and direction of the current in the 10 resistor in FIGURE EX28.4? b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling cw from V = 0 V at the lower left corner.

a. What are the magnitude and direction of the current in the 18 resistor in FIGURE EX28.5? b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling cw from V = 0 V at the lower left corner.

What is the magnitude of the potential difference across each resistor in FIGURE EX28.6?

What is the resistance of a 1500 W (120 V) hair dryer? What is the current in the hair dryer when it is used?

How much power is dissipated by each resistor in FIGURE EX28.8?

A 60 W lightbulb and a 100 W lightbulb are placed in the circuit shown in FIGURE EX28.9. Both bulbs are glowing. a. Which bulb is brighter? Or are they equally bright? b. Calculate the power dissipated by each bulb.

The five identical bulbs in FIGURE EX28.10 are all glowing. The battery is ideal. What is the order of brightness of the bulbs, from brightest to dimmest? Some may be equal. A. P = S 7 Q = R = T B. P = S = T 7 Q = R C. P 7 S = T 7 Q = R D. P 7 Q = R 7 S = T

The five identical bulbs in FIGURE EX28.11 are all glowing. The battery is ideal. What is the order of brightness of the bulbs, from brightest to dimmest? Some may be equal. A. P = T 7 Q = R = S B. P 7 Q = R = S 7 T C. P = T 7 Q 7 R = S D. P 7 Q 7 T 7 R = S

1 kWh is how many joules?

A standard 100 W (120 V) lightbulb contains a 7.0-cm-long tungsten filament. The high-temperature resistivity of tungsten is 9.0 * 10-7 m. What is the diameter of the filament?

A typical American family uses 1000 kWh of electricity a month. a. What is the average current in the 120 V power line to the house? b. On average, what is the resistance of a household?

A waterbed heater uses 450 W of power. It is on 25% of the time, off 75%. What is the annual cost of electricity at a billing rate of $0.12/kWh?

What is the value of resistor R in FIGURE EX28.16?

The battery in FIGURE EX28.17 is short-circuited by an ideal ammeter having zero resistance. a. What is the batterys internal resistance? b. How much power is dissipated inside the battery?

The circuit in FIGURE EX28.18 is called a voltage divider. What value of R will make Vout = Vin/10?

The voltage across the terminals of a 9.0 V battery is 8.5 V when the battery is connected to a 20 load. What is the batterys internal resistance?

Compared to an ideal battery, by what percentage does the batterys internal resistance reduce the potential difference across the 20 resistor in FIGURE EX28.20?

A variable resistor R is connected across the terminals of a battery. FIGURE EX28.21 shows the current in the circuit as R is varied. What are the emf and internal resistance of the battery?

Two of the three resistors in FIGURE EX28.22 are unknown but equal. The total resistance between points a and b is 75 . What is the value of R?

What is the value of resistor R in FIGURE EX28.23?

A metal wire of resistance R is cut into two pieces of equal length. The two pieces are connected together side by side. What is the resistance of the two connected wires?

What is the equivalent resistance between points a and b in FIGURE EX28.25?

What is the equivalent resistance between points a and b in FIGURE EX28.26?

What is the equivalent resistance between points a and b in FIGURE EX28.27?

What is the equivalent resistance between points a and b in FIGURE EX28.28?

The 10 resistor in FIGURE EX28.29 is dissipating 40 W of power. How much power are the other two resistors dissipating?

In FIGURE EX28.30, what is the value of the potential at points a and b?

In FIGURE EX28.31, what is the value of the potential at points a and b?

Show that the product RC has units of s.

What is the time constant for the discharge of the capacitors in FIGURE EX28.33?

What is the time constant for the discharge of the capacitors in FIGURE EX28.34?

A 10 mF capacitor initially charged to 20 mC is discharged through a 1.0 k resistor. How long does it take to reduce the capacitors charge to 10 mC?

The switch in FIGURE EX28.36 has been in position a for a long time. It is changed to position b at t =0 s. What are the charge Q on the capacitor and the current I through the resistor (a) immediately after the switch is closed? (b) at t =50 ms? (c) at t = 200 ms?

What value resistor will discharge a 1.0 mF capacitor to 10% of its initial charge in 2.0 ms?

A capacitor is discharged through a 100 resistor. The discharge current decreases to 25% of its initial value in 2.5 ms. What is the value of the capacitor?

It seems hard to justify spending $4.00 for a compact fluorescent lightbulb when an ordinary incandescent bulb costs 50. To see if this makes sense, compare a 60 W incandescent bulb lasting 1000 hours to a 15 W compact fluorescent bulb having a lifetime of 10,000 hours. Both bulbs produce the same amount of visible light and are interchangeable. If electricity costs $0.10/kWh, what is the total costpurchase plus energy to obtain 10,000 hours of light from each type of bulb? This is called the life-cycle cost.

A refrigerator has a 1000 W compressor, but the compressor runs only 20% of the time. a. If electricity costs $0.10/kWh, what is the monthly (30 day) cost of running the refrigerator? b. A more energy-efficient refrigerator with an 800 W compressor costs $100 more. If you buy the more expensive refrigerator, how many months will it take to recover your additional cost?

Two 75 W (120 V) lightbulbs are wired in series, then the combination is connected to a 120 V supply. How much power is dissipated by each bulb?

An electric eel develops a 450 V potential difference between its head and tail. The eel can stun a fish or other prey by using this potential difference to drive a 0.80 A current pulse for 1.0 ms. What are (a) the energy delivered by this pulse and (b) the total charge that flows?

You have a 2.0 resistor, a 3.0 resistor, a 6.0 resistor, and a 6.0 V battery. Draw a diagram of a circuit in which all three resistors are used and the battery delivers 9.0 W of power.

A 2.0-m-long, 1.0-mm-diameter wire has a variable resistivity given by r1x2 = 12.5 * 10-6 2c 1 + 1 x 1.0 m2 2 d m where x is measured from one end of the wire. What is the current if this wire is connected to the terminals of a 9.0 V battery?

What is the equivalent resistance between points a and b in FIGURE P28.45?

What are the emf and internal resistance of the battery in FIGURE P28.46?

A string of holiday lights can be wired in series, but all the bulbs go out if one burns out because that breaks the circuit. Most lights today are wired in series, but each bulb has a special fuse that short-circuits the bulbmaking a connection around itif it burns out, thus keeping the other lights on. Suppose a string of 50 lights is connected in this way and plugged into a 120 V outlet. By what factor does the power dissipated by each remaining bulb increase when the first bulb burns out?

The circuit shown in FIGURE P28.48 is inside a 15-cm-diameter balloon filled with helium that is kept at a constant pressure of 1.2 atm. How long will it take the balloons diameter to increase to 16 cm?

Suppose you have resistors 2.5 k, 3.5 k, and 4.5 k and a 100 V power supply. What is the ratio of the total power delivered to the resistors if they are connected in parallel to the total power delivered if they are connected in series?

A lightbulb is in series with a 2.0 resistor. The lightbulb dissipates 10 W when this series circuit is connected to a 9.0 V battery. What is the current through the lightbulb? There are two possible answers; give both of them

a. Load resistor R is attached to a battery of emf E and internal resistance r. For what value of the resistance R, in terms of E and r, will the power dissipated by the load resistor be a maximum? b. What is the maximum power that the load can dissipate if the battery has E = 9.0 V and r = 1.0 ?

The ammeter in FIGURE P28.52 reads 3.0 A. Find I1, I2, and E.

What is the current in the 2 resistor in FIGURE P28.53?

For an ideal battery 1r = 0 2, closing the switch in FIGURE P28.54 does not affect the brightness of bulb A. In practice, bulb A dims just a little when the switch closes. To see why, assume that the 1.50 V battery has an internal resistance r = 0.50 and that the resistance of a glowing bulb is R = 6.00 . a. What is the current through bulb A when the switch is open? b. What is the current through bulb A after the switch has closed? c. By what percentage does the current through A change when the switch is closed?

What are the battery current Ibat and the potential difference Va - Vb between points a and b when the switch in FIGURE P28.55 is (a) open and (b) closed?

A battery is a voltage source, always providing the same potential difference regardless of the current. It is possible to make a current source that always provides the same current regardless of the potential difference. The circuit in FIGURE P28.56 is called a current divider. It sends a fraction of the source current to the load. Find an expression for Iload in terms of R1, R2, and Isource . You can assume that the loads resistance is much less than R2 .

A circuit youre building needs an ammeter that goes from 0 mA to a full-scale reading of 50 mA. Unfortunately, the only ammeter in the storeroom goes from 0 mA to a full-scale reading of only 500 mA. Fortunately, youve just finished a physics class, and you realize that you can make this ammeter work by putting a resistor in parallel with it, as shown in FIGURE P28.57. Youve measured that the resistance of the ammeter is 50.0 , not the 0 of an ideal ammeter. a. What value of R must you use so that the meter will go to full scale when the current I is 50 mA? b. What is the effective resistance of your ammeter?

For the circuit shown in FIGURE P28.58, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading

For the circuit shown in FIGURE P28.59, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

For the circuit shown in FIGURE P28.60, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

What is the current through the 20 resistor in FIGURE P28.61?

For the circuit shown in FIGURE P28.62, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

What is the current through the 10 resistor in FIGURE P28.63? Is the current from left to right or right to left?

For what emf E does the 200 resistor in FIGURE P28.64 dissipate no power? Should the emf be oriented with its positive terminal at the top or at the bottom?

A 12 V car battery dies not so much because its voltage drops but because chemical reactions increase its internal resistance. A good battery connected with jumper cables can both start the engine and recharge the dead battery. Consider the automotive circuit of FIGURE P28.65. a. How much current could the good battery alone drive through the starter motor? b. How much current is the dead battery alone able to drive through the starter motor? c. With the jumper cables attached, how much current passes through the starter motor? d. With the jumper cables attached, how much current passes through the dead battery, and in which direction?

How much current flows through the bottom wire in FIGURE P28.66, and in which direction?

The capacitor in an RC circuit is discharged with a time constant of 10 ms. At what time after the discharge begins are (a) the charge on the capacitor reduced to half its initial value and (b) the energy stored in the capacitor reduced to half its initial value?

A circuit youre using discharges a 20 mF capacitor through an unknown resistor. After charging the capacitor, you close a switch at t = 0 s and then monitor the resistor current with an ammeter. Your data are as follows: Time (s) Current 1MA2 0.5 890 1.0 640 1.5 440 2.0 270 2.5 200 Use an appropriate graph of the data to determine (a) the resistance and (b) the initial capacitor voltage.

A 150 mF defibrillator capacitor is charged to 1500 V. When fired through a patients chest, it loses 95% of its charge in 40 ms. What is the resistance of the patients chest?

A 50 mF capacitor that had been charged to 30 V is discharged through a resistor. FIGURE P28.70 shows the capacitor voltage as a function of time. What is the value of the resistance?

A 0.25 mF capacitor is charged to 50 V. It is then connected in series with a 25 resistor and a 100 resistor and allowed to discharge completely. How much energy is dissipated by the 25 resistor?

A 70 mF capacitor is discharged through two parallel resistors, 15 k and 25 k. By what factor will the time constant of this circuit increase if the resistors are instead placed in series with each other?

The capacitor in FIGURE P28.73 begins to charge after the switch closes at t = 0 s. a. What is VC a very long time after the switch has closed? b. What is Qmax in terms of E, R, and C? c. In this circuit, does I = +dQ/dt or -dQ/dt? Explain. d. Find an expression for the current I at time t. Graph I from t = 0 to t = 5t

The capacitors in FIGURE P28.74 are charged and the switch closes at t = 0 s. At what time has the current in the 8 resistor decayed to half the value it had immediately after the switch was closed?

The flash on a compact camera stores energy in a 120 mF capacitor that is charged to 220 V. When the flash is fired, the capacitor is quickly discharged through a lightbulb with 5.0 of resistance. a. Light from the flash is essentially finished after two time constants have elapsed. For how long does this flash illuminate the scene? b. At what rate is the lightbulb dissipating energy 250 ms after the flash is fired? c. What total energy is dissipated by the lightbulb?

Large capacitors can hold a potentially dangerous charge long after a circuit has been turned off, so it is important to make sure they are discharged before you touch them. Suppose a 120 mF capacitor from a camera flash unit retains a voltage of 150 V when an unwary student removes it from the camera. If the student accidentally touches the two terminals with his hands, and if the resistance of his body between his hands is 1.8 k, for how long will the current across his chest exceed the danger level of 50 mA?

Digital circuits require actions to take place at precise times, so they are controlled by a clock that generates a steady sequence of rectangular voltage pulses. One of the most widely used integrated circuits for creating clock pulses is called a 555 timer. FIGURE P28.77 shows how the timers output pulses, oscillating between 0 V and 5 V, are controlled with two resistors and a capacitor. The circuit manufacturer tells users that TH, the time the clock output spends in the high 15 V2 state, is TH = 1R1 + R22C * ln 2. Similarly, the time spent in the low 10 V2 state is TL = R2C * ln 2. You need to design a clock that will oscillate at 10 MHz and will spend 75% of each cycle in the high state. You will be using a 500 pF capacitor. What values do you need to specify for R1 and R2?

What power is dissipated by the 2 resistor in FIGURE CP28.78?

Youve made the finals of the Science Olympics! As one of your tasks, youre given 1.0 g of aluminum and asked to make a wire, using all the aluminum, that will dissipate 7.5 W when connected to a 1.5 V battery. What length and diameter will you choose for your wire?

The switch in FIGURE CP28.80 has been closed for a very long time. a. What is the charge on the capacitor? b. The switch is opened at t = 0 s. At what time has the charge on the capacitor decreased to 10% of its initial value?

The capacitor in Figure 28.38a begins to charge after the switch closes at t = 0 s. Analyze this circuit and show that Q = Qmax11 - e-t/t 2, where Qmax = CE

The switch in Figure 28.38a closes at t = 0 s and, after a very long time, the capacitor is fully charged. Find expressions for (a) the total energy supplied by the battery as the capacitor is being charged, (b) total energy dissipated by the resistor as the capacitor is being charged, and (c) the energy stored in the capacitor when it is fully charged. Your expressions will be in terms of E, R, and C. (d) Do your results for parts a to c show that energy is conserved? Explain

An oscillator circuit is important to many applications. A simple oscillator circuit can be built by adding a neon gas tube to an RC circuit, as shown in FIGURE CP28.83. Gas is normally a good insulator, and the resistance of the gas tube is essentially infinite when the light is off. This allows the capacitor to charge. When the capacitor voltage reaches a value Von, the electric field inside the tube becomes strong enough to ionize the neon gas. Visually, the tube lights with an orange glow. Electrically, the ionization of the gas provides a very-low-resistance path through the tube. The capacitor very rapidly (we can think of it as instantaneously) discharges through the tube and the capacitor voltage drops. When the capacitor voltage has dropped to a value Voff, the electric field inside the tube becomes too weak to sustain the ionization and the neon light turns off. The capacitor then starts to charge again. The capacitor voltage oscillates between Voff, when it starts charging, and Von, when the light comes on to discharge it. a. Show that the oscillation period is T = RC ln1 E - Voff E - Von 2 b. A neon gas tube has Von = 80 V and Voff = 20 V. What resistor value should you choose to go with a 10 mF capacitor and a 90 V battery to make a 10 Hz oscillator?