Page 31 - Schaum's Outline of Theory and Problems of Electric Circuits

CIRCUIT CONCEPTS
[CHAP. 2
20
3
2.15 A resistance of 5.0
has a current i ¼ 5:0 10 t (A) in the interval 0 t 2 ms. Obtain the instantaneous
2
and average power. Ans. 125.0t (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. 6:4mA

3
2.17 Determine the single circuit element for which the current and voltage in the interval 0 10 t are given
3
3
by i ¼ 2:0 sin 10 t (mA) and v ¼ 5:0 cos 10 t (mV). Ans. An inductance of 2.5 mH
3
10 t
2.18 An inductance of 4.0 mH has a voltage v ¼ 2:0e (V). Obtain the maximum stored energy. At t ¼ 0,
the current is zero. Ans. 0.5 mW
2.19 A capacitance of 2.0 mF with an initial charge Q 0 is switched into a series circuit consisting of a 10.0-
resistance. Find Q 0 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 ¼ðV m =RÞe t=ðRcÞ (A), show that the maximum stored
2
1
energy is CV m . Assume the initial charge is zero.
2
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 Qð0Þ¼ 0.
Ans.(a)25 V; (b) 75 V; (c) 81.3 V

Fig. 2-20

t=0:015
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 (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 v 2 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) 5A

2.24 In the circuit shown in Fig. 2-23, find the current, i, given (a) i 1 ¼ 2A, i 2 ¼ 0; (b) i 1 ¼ 1A; i 2 ¼ 4A;
(c) i 1 ¼ i 2 ¼ 1A. Ans. (a)10 A; (b)11 A; (c)9A

2.25 A1-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