20

CIRCUIT CONCEPTS

[CHAP. 2

2.15

A resistance of 5.0  has a current i ¼ 5:0  103 t (A) in the interval 0  t  2 ms. and average power. Ans. 125.0t2 (W), 167.0 (W)

2.16

Current i enters a generalized circuit element at the positive terminal and the voltage across the element is 3.91 V. If the power absorbed is 25:0 mW, obtain the current. Ans. 6:4 mA

2.17

Determine the single circuit element for which the current and voltage in the interval 0  103 t   are given by i ¼ 2:0 sin 103 t (mA) and v ¼ 5:0 cos 103 t (mV). Ans. An inductance of 2.5 mH

2.18

An inductance of 4.0 mH has a voltage v ¼ 2:0e10 t (V). Obtain the maximum stored energy. the current is zero. Ans. 0.5 mW

2.19

A capacitance of 2.0 mF with an initial charge Q0 is switched into a series circuit consisting of a 10.0- resistance. Find Q0 if the energy dissipated in the resistance is 3.6 mJ. Ans. 120.0 mC

2.20

Given that a capactance of C farads has a current i ¼ ðVm =RÞet=ðRcÞ (A), show that the maximum stored energy is 12 CVm2 . Assume the initial charge is zero.

2.21

The current after t ¼ 0 in a single circuit element is as shown in Fig. 2-20. Find the voltage across the element at t ¼ 6:5 ms, if the element is (a) 10 k, (b) 15 mH, (c) 0.3 nF with Qð0Þ ¼ 0. Ans. (a) 25 V; (b) 75 V; (c) 81.3 V

3

Obtain the instantaneous

At t ¼ 0,

Fig. 2-20 2.22

The 20.0-mF capacitor in the circuit shown in Fig. 2-21 has a voltage for t > 0, v ¼ 100:0et=0:015 (V). Obtain the energy function that accompanies the discharge of the capacitor and compare the total energy to that which is absorbed by the 750- resistor. Ans. 0.10 ð1  et=0:0075 Þ (J)

Fig. 2-21 2.23

Find the current i in the circuit shown in Fig. 2-22, if the control v2 of the dependent voltage source has the value (a) 4 V, (b) 5 V, (c) 10 V. Ans. (a) 1 A; (b) 0 A; (c) 5 A

2.24

In the circuit shown in Fig. 2-23, ﬁnd the current, i, given (a) i1 ¼ 2 A, i2 ¼ 0; (c) i1 ¼ i2 ¼ 1 A. Ans. (a) 10 A; (b) 11 A; (c) 9A

2.25

A 1-mF capacitor with an initial charge of 104 C is connected to a resistor R at t ¼ 0. Assume discharge current during 0 < t < 1 ms is constant. Approximate the capacitor voltage drop at t ¼ 1 ms for

(b) i1 ¼ 1 A; i2 ¼ 4 A;

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An