(a) To determine Calculate the branch currents i 1 , i 2 , and i 3 in the given circuit using mesh-current method. Explanation The given circuit is redrawn as shown in Figure 1. Apply Kirchhoff’s voltage law for loop current i a in Figure 1. − 30 = ( 5 k ) i a + 500 ( i a − i c ) − 30 = 5000 i a + 500 i a − 500 i c { ∵ 1 k = 10 3 } − 30 = 5500 i a − 500 i c (1) Apply Kirchhoff’s voltage law for loop current i d in Figure 1. − 80 = ( 4 k ) ( i d − i c ) − 80 = 4 000 ( i d − i c ) { ∵ 1 k = 10 3 } − 80 = − 4000 i c + 4 000 i d (2) From Figure 1 the two supermesh equations are as follows. i c − i b = 10 m i c − i b = 10 × 10 − 3 { ∵ 1 m = 10 − 3 } i c − i b = 0.01 (3) 0 = ( 1 k ) i b + ( 4 k ) ( i c − i d ) + 500 ( i c − i a ) 0 = 1 000 i b + 4 000 i c − 4000 i d + 500 i c − 500 i a { ∵ 1 k = 10 3 } 0 = − 500 i a + 1 000 i b + 4 500 i c − 4000 i d (4) Rearrange the equation (4) as follows, 500 i a = 1 000 i b + 4 500 i c − 4000 i d i a = 1 000 i b + 4 500 i c − 4000 i d 500 i a = 2 i b + 9 i c − 8 i d (5) Rearrange the equation (1) as follows, 500 i c = 5500 i a + 30 i c = 5500 i a + 30 500 i c = 11 i a + 0.06 (6) Rearrange the equation (3) as follows, i c = 0.01 + i b (7) Substitute equation (7) in equation (6). 0.01 + i b = 11 i a + 0.06 i b = 11 i a + 0.06 − 0.01 i b = 11 i a + 0.05 (8) Rearrange the equation (2) as follows;. 4 000 i d = − 80 + 4000 i c i d = − 80 + 4000 i c 4 000 i d = − 0.02 + i c (9) Substitute equation (6) in equation (9). i d = − 0.02 + 11 i a + 0.06 i d = 0.04 + 11 i a (10) Substitute equation (6), (8) and (10) in equation (5) to find the current i a in amperes (b) To determine Prove that the total power dissipated in the circuit is equal to the power developed in the circuit.

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 4, Problem 49P

(a)

To determine

Calculate the branch currents i1, i2, and i3 in the given circuit using mesh-current method.

(b)

To determine

Prove that the total power dissipated in the circuit is equal to the power developed in the circuit.

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Chapter 4, Problem 48P

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I need help checking if its correct -E1 + VR1 + VR4 – E2 + VR3 = 0 -------> Loop 1 (a) R1(I1) + R4(I1 – I2) + R3(I1) = E1 + E2 ------> Loop 1 (b) R1(I1) + R4(I1) - R4(I2) + R3(I1) = E1 + E2 ------> Loop 1 (c) (R1 + R3 + R4) (I1) - R4(I2) = E1 + E2 ------> Loop 1 (d) Now that we have loop 1 equation will procced on finding the equation of I2 current loop. However, a reminder that because we are going in a clockwise direction, it goes against the direction of the current. As such we will get an equation for the matrix that will be: E2 – VR4 – VR2 + E3 = 0 ------> Loop 2 (a) -R4(I2 – I1) -R2(I2) = -E2 – E3 ------> Loop 2 (b) -R4(I2) + R4(I1) - R2(I2) = -E2 – E3 -----> Loop 2 (c) R4(I1) – (R4 + R2)(I2) = -E2 – E3 -----> Loop 2 (d) These two equations will be implemented to the matrix formula I = inv(A) * b R11 R12 (R1 + R3 + R4) -R4 -R4 R4 + R2

10.2 For each of the following groups of sources, determineif the three sources constitute a balanced source, and if it is,determine if it has a positive or negative phase sequence.(a) va(t) = 169.7cos(377t +15◦) Vvb(t) = 169.7cos(377t −105◦) Vvc(t) = 169.7sin(377t −135◦) V(b) va(t) = 311cos(wt −12◦) Vvb(t) = 311cos(wt +108◦) Vvc(t) = 311cos(wt +228◦) V(c) V1 = 140 −140◦ VV2 = 114 −20◦ VV3 = 124 100◦ V

Apply single-phase equivalency to determine the linecurrents in the Y-D network shown in Fig. P10.13. The loadimpedances are Zab = Zbc = Zca = (25+ j5) W

Chapter 4 Solutions

Electric Circuits. (11th 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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