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i The powers absorbed by the sources are: 20 50 10 A 3
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Fig. 2-18 pa va i 20 10 200 W pb vb i 50 10 500 W Since power delivered is the negative of power absorbed, source vb delivers 500 W and source va absorbs 200 W. The power in the two resistors is 300 W.
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A 25.0- resistance has a voltage v 150:0 sin 377t (V). Find the power p and the average power pavg over one cycle.
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i v=R 6:0 sin 377t A p vi 900:0 sin2 377t W The end of one period of the voltage and current functions occurs at 377t 2. integration is taken over one-half cycle, 377t . Thus, 1  Pavg 900:0 sin2 377t d 377t 450:0 W  0 For Pavg the
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Find the voltage across the 10.0- resistor in Fig. 2-19 if the control current ix in the dependent source is (a) 2 A and (b) 1 A.
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i 4ix 4:0; vR iR 40:0ix 40:0 V ix 2; vR 40:0 V ix 1; vR 80:0 V
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2.14 A resistor has a voltage of V 1:5 mV. (b) 1.20 mW. Ans. 18.5 mA, 0.8 mA Obtain the current if the power absorbed is (a) 27.75 nW and
CIRCUIT CONCEPTS
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A resistance of 5.0  has a current i 5:0 103 t (A) in the interval 0 ! t ! 2 ms. and average power. Ans. 125.0t2 (W), 167.0 (W)
Obtain the instantaneous
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 Determine the single circuit element for which the current and voltage in the interval 0 ! 103 t !  are given by i 2:0 sin 103 t (mA) and v 5:0 cos 103 t (mV). Ans. An inductance of 2.5 mH An inductance of 4.0 mH has a voltage v 2:0e 10 t (V). Obtain the maximum stored energy. the current is zero. Ans. 0.5 mW
At t 0,
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 Given that a capactance of C farads has a current i Vm =R e t= Rc (A), show that the maximum stored 2 energy is 1 CVm . Assume the initial charge is zero. 2 The current after t 0 in a single circuit element is as shown in Fig. 2-20. Find the voltage across the element at t 6:5 ms, if the element is (a) 10 k, (b) 15 mH, (c) 0.3 nF with Q 0 0. Ans. (a) 25 V; (b) 75 V; (c) 81.3 V
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 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 1 e t=0:0075 (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 In the circuit shown in Fig. 2-23, nd the current, i, given (a) i1 2 A, i2 0; (c) i1 i2 1 A. Ans. (a) 10 A; (b) 11 A; (c) 9A (b) i1 1 A; i2 4 A;
A 1-mF capacitor with an initial charge of 10 4 C is connected to a resistor R at t 0. Assume discharge current during 0 < t < 1 ms is constant. Approximate the capacitor voltage drop at t 1 ms for
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