Consider the circuit shown in the figure (Figure 1). Suppose the four resistors

Question

Consider the circuit shown in the figure (Figure 1). Suppose the four resistors in this circuit have the values R_1 = 13 Ohm, R_2 = 8.0 Ohm, R_3 = 7.6 Ohm, and R_4 = 15 Ohm, and that the emf of the battery is epsilon = 15 V. Find the current through each resistor using the rules for series and parallel resistors. Express your answers using two significant figures separated by commas. Find the current through each resistor using Kirchhoff's rules. Express your answers using two significant figures separated by commas.

Explanation / Answer

PART A

R1 = 13 , R2 = 8 , R3 = 7.6 , R4 = 15

Req = R1 + [R3 II (R2 + R4)]

=> Req = 13 + [7.6 II 23] = 13 + [7.6*23/(7.6+23)] = 18.71

I1 = /Req = 15/18.71

=>I1 = 0.8 A

Let I2 = I4 = I

I = R3I1/(R3 + R2 + R4)

=> I = 0.2 A = I2 = I4

I3 =  (R2+R4)I1/(R3 + R2 + R4)

=> I3 = 0.6 A

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PART B

let i be the current in the left loop in clockwise direction and I be the current in the right loop in anticlockwise direction

- R3(i+I) - R1i = 0

R3(i+I) + (R2 + R4)I = 0

Solving we get,

i = 0.8 A

I = -0.2 A

I1 = 0.8 A

I2 = I4 = I = 0.2 A

I3 = I + i = 0.6 A

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