Consider the circuit shown in Figure 7.1.2. Let I1, I2,

Chapter 7, Problem 19

(choose chapter or problem)

Consider the circuit shown in Figure 7.1.2. Let I1, I2, and I3 be the currents through thecapacitor, resistor, and inductor, respectively. Likewise, let V1, V2, and V3 be the correspondingvoltage drops. The arrows denote the arbitrarily chosen directions in whichcurrents and voltage drops will be taken to be positive.(a) Applying Kirchhoffs second law to the upper loop in the circuit, show thatV1 V2 = 0. (i)In a similar way, show thatV2 V3 = 0. (ii)(b) Applying Kirchhoffs first law to either node in the circuit, show thatI1 + I2 + I3 = 0. (iii)(c) Use the currentvoltage relation through each element in the circuit to obtain theequationsCV1 = I1, V2 = RI2, LI3 = V3. (iv)(d) Eliminate V2, V3, I1, and I2 among Eqs. (i) through (iv) to obtainCV1 = I3 V1R , LI3 = V1. (v)Observe that if we omit the subscripts in Eqs. (v), then we have the system (2) of thissection