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

Question

A circuit is constructed with five resistors and a battery as shown. The values for the resistors are: R1 = R5 = 71 ?, R2 = 139 ?, R3 = 101 ?, and R4 = 125 ?. The battery voltage is V = 12 V.

1) What is Rab, the equivalent resistance between points a and b?

2) What is Rac, the equivalent resistance between points a and c?

3) What is I5, the current that flows through resistor R5?

4) What is I2, the current that flows through resistor R2?

5) What is I1, the current that flows through the resistor R1?

6) What is V4, the voltage across resistor R4?

Explanation / Answer

Here

a) for the resistance between points a and b

Rab = R4 || ( R2 + R3)

Rab = 125 * (139+101)/(139 + 101 + 125)

Rab = 82.2 Ohm

the resistance Rab is 82.2 Ohm

b)

between the point a and c

Rac = Rab + R1

Rac = 82.2 + 71

Rac = 153.2 Ohm

the resistance Rac is 153.2 Ohm

c)

Now, for the current i5

Req = Rac + R4 = 153.2 + 71

Req = 224.2 Ohm

I5 = 12/224.2

I5 = 0.0535 A

the current I5 is 0.0535 A

d)

current in I2 = I5 * Rab /(R2 + R3)

current I2 = 0.0535 * 82.2/(139+101)

current I2 = 0.0183 A

5)

I1 = I5

I1 = 0.0535 A

6)

V4 = Rab * I5

V4 = 0.0535 * 82.2

V4 = 4.4 V

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