Find the currents through each resistor in the circuit shown on the diagram (Fig

Question

Find the currents through each resistor in the circuit shown on the diagram (Figure 1) . Use the following values: E = 12.0V , R 1   = 35.0? , R 2   = 22.0? , R 3   = 41.0? , and R 4   = 14.0? .

Find the following currents:

the current I 1   through the resistor of resistance R 1   = 35.0?

the current I 2   through the resistor of resistance R 2   = 22.0?

the current I 3   through the resistor of resistance R 3   = 41.0?

the current I 4   through the resistor of resistance R 4   = 14.0?

Find the currents through each resistor in the circuit shown on the diagram (Figure 1) . Use the following values: E = 12.0V , R 1 = 35.0? , R 2 = 22.0? , R 3 = 41.0? , and R 4 = 14.0? . Find the following currents: the current I 1 through the resistor of resistance R 1 = 35.0? the current I 2 through the resistor of resistance R 2 = 22.0? the current I 3 through the resistor of resistance R 3 = 41.0? the current I 4 through the resistor of resistance R 4 = 14.0?

Explanation / Answer

Let there be two loops , loop 1 and loop 2 with current I1 and I2

Now for loop 1

35 I1 + 22(I1-I2) +12 = 0

=> 57 I1 -22 I2 = -12 ---------(1)

loop 2

41I2 +14I2 +22 (I2-I1) = 12

=> -22 I1 + 77I2 = 12                   (2)

On solving 1 and 2

we get

I1 =    -0.1690A               i2 = 0.10755 A

the current I 1   through the resistor of resistance R 1   = 35.0 = 0.1690 A (ans)

the current I 2   through the resistor of resistance R 2   = 22.0 = I1- I2 = 0.1690 + 0.10755 = 0.27655 A (ans)

the current I 3   through the resistor of resistance R 3   = 41.0 = 0.10755 A (ans)

the current I 4   through the resistor of resistance R 4   = 14.0 = 0.10755A (ans)

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