Circuit 1 with Resistors and a Battery 1 2 3 4 5 6 7 A circuit is constructed wi

Question

Circuit 1 with Resistors and a Battery

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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 = 130 , and R4 = 108 . 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?

A

2)

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

V

3)

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

A

4)

What is RX, the value of the unknown resistor RX?

5)

What is V1, the magnitude of the voltage across the resistor R1?

Explanation / Answer

1)

R1 and R3 are in series and their combination is given as

R13 = R1 + R3 = 50 + 130 = 180 ohm

the battery Voltage is in parallel with R13 , hence

i13 = i1 = current in R1 = V/R13 = 12/180 = 0.067 A

5)

V1 = i1 R1 = 0.067 x 50 = 3.35 volts

4)

R1/R3 = R2 /Rx

50/130 = 129/Rx

Rx = 335.4 ohm

3)

R2 and Rx are in series and their combination is given as

R2x = R2 + Rx = 129 + 335.4 = 464.4 ohm

the battery Voltage is in parallel with R2x , hence

i2x = i2 = current in R2 = V/R2x = 12/464.4 = 0.026 A

2)

V2 = i2 R2 = 0.026 x 129 = 3.4 volts

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