A circuit is constructed with six resistors and two batteries as shown. The batt

Question

A circuit is constructed with six resistors and two batteries as shown. The battery voltages are V1 = 18 V and V2 = 12 V. The positive terminals are indicated with a + sign, The values for the resistors are: R1 = R5 = 46 ?, R2 = R6 = 144 ? R3 = 115 ?, and R4 = 90 ?. The positive directions for the currents I1, I2 and I3 are indicated by the directions of the arrows

1- What is I3, the current that flows through the resistor R3? A positive value for the current is defined to be in the direction of the arrow?

2-What is I2, the current that flows through the resistor R2? A positive value for the current is defined to be in the direction of the arrow.?

3-What is I1, the current that flows through the resistor R1? A positive value for the current is defined to be in the direction of the arrow.?

4-What is V(a) – V(b), the potential difference between the points a and b?

.

Explanation / Answer

here,

using KCL

I2 = I1 + I3 ....(1)

and

using KVL in the left loop

I1*R1 - I3*R3 = V1 ....(2)

and

ussing KVL in the middle loop

I3 * R3 + I2 * R6 + I2 * R2 = V2 - V1

115 * I3 + 144*I2 + 144*I2 = 12 - 18 ....(3)

from(1) , (2) and (3)

1)

I1 = 0.127 A

2)

I2 = 0.021 A

3)

I3 = - 0.106 A

4)

V(a) - V(b) = R6 * I2 = 144 * 0.021 = 3.02 V

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