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 = 49 , R2 = 151 , R3 = 45 , and R4 = 93 . The battery voltage is V = 12 V.

1)

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

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2)

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

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3)

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

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4)

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

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5)

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

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6)

What is V4, the voltage across resistor R4?

V

Explanation / Answer

Here ,

1) for the equivalent resistance

Rab = (R4) || (R2 + R3)

Rab = 93 || (151 + 45)

Rab = 93 || 196

Rab = 93 * 196/( 93 + 196) = 63.1 Ohm

the equivalent resistance between a and b is 63.1 Ohm

2)

for the Rac

resistance R1 is in series with Rab

Rac = Rab + R1

Rac = 63.1 + 49

Rac = 112.1 Ohm

the equivalent resistance between a and c is 112.1 Ohm

3)

for the current through R5

current I5 = V/(R5 + Rab)

current I5 = 12/(112.1 + 49)

current I5 = 0.0745 A

the current I5 is 0.0745 A

4)
for the current in R2

Using current divider,

I2 = R4 * I5/(R2 + R3 + R4)

I2 = 93 * 0.0745/(151 + 45 + 93)

I2 = 0.024 A

the current I2 is 0.024 A

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