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 = 78 ?, R2 = 144 ?, R3 = 110 ?, and R4 = 63 ?. 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

We can see in the circuit that resistance R2 & R3 are in series and balance all resistance R1, R4 & R5 are in parallel and they are also in parallel to R2 & R3

1. Rab = (R2 + R3)* R4/ (R2 + R3 + R4) = 254*63/ 317 = 50.479 ohm.......Ans.

2.Rac =50.549*78/128.549 = 30.63 ohm....Ans.

3. Total resistance of the circuit = 30.63*78/108.63 = 22.00 ohm

hence I = 12/22 = 0.5456 amp....Ans.

4. I2 = 12/254 = 0.0472 amp......Ans.

5.I1 = 12/78 =0.153 amp.......Ans.

6. V4 = 12 volt

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