A circuit is constructed with five resistors and a battery as shown. The battery

Question

A circuit is constructed with five resistors and a battery as shown. The battery voltage is V = 12 V. The values for the resistors are: R1 = 50 , R2 = 129 , R3 = 170 , and R4 = 68 . The value for RX is unknown, but it is known that I4, the current that flows through resistor R4, is zero.

1.) What is I1, the magnitude of the current that flows through the resistor R1?

2.) What is V2, the magnitude of the voltage across the resistor R2?

3.) What is I2, the magnitude of the current that flows through the resistor R2?

Explanation / Answer

The resistance configuration that results in I4 = 0 is wheatstone bridge configuration and we can neglect R4 from the circuit.

=> R1/R3 = R2/Rx

=> Rx = R2R3/R1 = (129*170)/50 = 438.6 ohm

1. effective resistance of R1 and R3 = 50+170 = 220 ohm

effective resistance of R2 and Rx = 129+438.6 = 567.6 ohm

Effective resistance of complete circuit = (220*567.6)/(220+567.6) = 158.55 ohm

Total current = 12/158.55 = 0.075687 A

So current I1 through R1 = 12 / 220 = 0.0545 A

2. V2, voltage across R2 = Voltage across R1 = 0.0545 * 50 = 2.727 V

3. I2, the magnitude of the current that flows through the resistor R2 = 12/567.6 = 0.02114 A

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