(a) Explanation Given data: Refer to Figure given in the textbook. The load with resistance R Ω . The distance between the load and the source v 1 is x . The equal distance between the sources is L . Calculation: In Figure 1, apply nodal analysis as follows, v − v 1 2 x r + v R + v − v 2 2 r ( L − x ) = 0 v 2 x r − v 1 2 x r + v R + v 2 r ( L − x ) − v 2 2 r ( L − x ) = 0 v 2 x r + v R + v 2 r ( L − x ) = v 1 2 x r + v 2 2 r ( L − x ) v [ 1 2 x r + 1 2 r ( L − x ) + 1 R ] = 1 2 r [ v 1 x + v 2 ( L − x ) ] Simplifying the above equation as follows, v [ 1 2 r ( 1 x + 1 ( L − x ) ) + 1 R ] = 1 2 r [ v 1 x + v 2 ( L − x ) ] v [ 1 2 r ( L − x + x x ( L − x ) ) + 1 R ] = 1 2 r [ ( L − x ) v 1 + x v 2 x ( L − x ) ] v [ L 2 r x ( L − x ) + 1 R ] = 1 2 r [ L v 1 − x v 1 + x v 2 x ( L − x ) ] v [ L R + 2 r x ( (b) To determine Prove that the voltage v will be minimum when x = L v 2 − v 1 [ − v 1 ± v 1 v 2 − R 2 r L ( v 1 − v 2 ) 2 ] . (c) To determine Find the value of distance x derived in Part (b). (d) To determine Find the minimum value of voltage v derived in Part (a).

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ISBN: 9781292060545

Author: James W. Nilsson, Susan Riedel

Publisher: Pearson Education Limited

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Chapter 4, Problem 102P

(a)

To determine

Prove that the voltage v=v1RL+R(v2−v1)xRL+2rLx−2rx2 for the given circuit.

(b)

To determine

Prove that the voltage v will be minimum when x=Lv2−v1[−v1±v1v2−R2rL(v1−v2)2].

(c)

To determine

Find the value of distance x derived in Part (b).

(d)

To determine

Find the minimum value of voltage v derived in Part (a).

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Chapter 4, Problem 101P

Chapter 4, Problem 103P

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Chapter 4 Solutions

Electric Circuits, Global Edition

Ch. 4.2 - a) For the circuit shown, use the node-voltage...Ch. 4.2 - Use the node-voltage method to find v in the...Ch. 4.3 - Use the node-voltage method to find the power...Ch. 4.4 - Use the node-voltage method to find vo in the...Ch. 4.4 - Use the node-voltage method to find v in the...Ch. 4.4 - Use the node-voltage method to find v1 in the...Ch. 4.5 - Use the mesh-current method to find (a) the power...Ch. 4.6 - Determine the number of mesh-current equations...Ch. 4.6 - Use the mesh-current method to find vo in the...Ch. 4.7 - Use the mesh-current method to find the power...

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Prove that the voltage v = v 1 R L + R ( v 2 − v 1 ) x R L + 2 r L x − 2 r x 2 for the given circuit.

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Prove that the voltage v=v1RL+R(v2−v1)xRL+2rLx−2rx2 for the given circuit.

Prove that the voltage v will be minimum when x=Lv2−v1[−v1±v1v2−R2rL(v1−v2)2].

Find the value of distance x derived in Part (b).

Find the minimum value of voltage v derived in Part (a).

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Chapter 4 Solutions