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 = 54 ?, R2 = 132 ?, R3 = 136 ?, and R4 = 110 ?. 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?

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

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

6)If the value of the resistor R2 were doubled, how would the value of the resistor R3 have to change in order to keep the current through R4 equal to zero?

Explanation / Answer

Here,

for R1 = 54 Ohm , R2 = 132 Ohm

R3 = 136 Ohm

R4 = 110 Ohm

a) for the current in R1

I1 = V/(R1 + R2)

I1 = 12/(54 + 136)

I1 = 0.0631 A

the magnitude of current I1 is 0.0631 A

b)

as the current in R2 is zero

the potential across the R2 is equal to R1

V2 = I1 * R1

V2 = 0.0631 * 54 V

V2 = 3.41 V

c)

for the current in R2

I2 = V2/R2

I2 = 3.41/(132)

I2 = 0.0258 A

the current I2 is 0.0258 A

d)

for the resistance Rx

V - I2 * R2 - I2 * Rx = 0

12 - 0.0258 * 132 - 0.0258 - Rx =0

Rx = 332.9 Ohm

the resistance Rx is 332.9 Ohm

e)

magnitude of voltage across R1 = V2

magnitude of voltage across R1 = 3.41 V

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