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Draw two graphs of charge versus time on a capacitor. Draw
Chapter 21, Problem 33(choose chapter or problem)
Problem 33CQ
Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.38, starting from t = 0 . Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.39, starting at t = 0 , with an initial charge Q0 . Show at least two intervals of τ .
Questions & Answers
QUESTION:
Problem 33CQ
Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.38, starting from t = 0 . Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.39, starting at t = 0 , with an initial charge Q0 . Show at least two intervals of τ .
ANSWER:
Solution 33CQ
The expression for voltage as a function of time is given by:
V = emf ( 1-e )
The graph of voltage versus time will then be of the form:
Step 3 of 9
Recall that charge stored in a capacitor is given by:
Q=CV
Here Q is the charge, V is the voltage across the capacitor and C is the capacitance. Using this relation and the function above, the expression for charge as function of time will be:
Q=emf ( 1-e
)
Q = C (emf ) ( 1-e )
=Q0 ( 1-e )
Here Q0 is the charge stored in the capacitor when voltage across it reaches the maximum value.