A. A curcuit has three resistors connected to a 3V battery in series: R1= 15 Ohm

Question

A. A curcuit has three resistors connected to a 3V battery in series: R1= 15 Ohms, R2=10 Ohms, R3= 25 Ohms. Find the equivalent resistance, the total current in the circuit, and the voltage across each resistor.

B. The same resistor are not connected to the 3V battery in parallel. Find the equivalent resistance, the total current in the circuit, and the current through each resistor.

C. A fourth resistor R4= 13 Ohms is now added and the four resistor are arranged according to the diagram below. Find the equivalent resistance, the total current in the circuit, the current through each resistor, and the voltage across each resistor

Explanation / Answer

A. when connected in series,

Req = R1 + R2 + R3 = 15 + 10 + 25 = 50 ohm .....Ans

total current, I = V / Req = 3 / 50 = 0.06 A

V1 = I R1 = 0.9 V

V2 = 0.06 x 10 = 0.6 V

V3 = 0.06 x 25 = 1.5 V

B. when connected in parallel.

1/Req = 1/15 + 1/10 + 1/25

Req = 4.84 Ohm

I = V/ Req = 3/ 4.84 = 0.62 A

Voltage across each resistor will be 3V.

I1 = 3/15 = 0.2 A

I2 = 3/10 = 0.3 A

I3 = 3/25 = 0.12 A

C. R2 and R3 are in parallel connection.

1/R' = 1/R2 + 1/R3 = 1/10 + 1/25

R' = 7.14 ohm

now R1, R' and R4 are in series.

Req = R1 + R' + R4 = 15 + 7.14 + 13 = 35.14 Ohm

I = 3 / 35.14 = 0.085 A

I1 = I4 = 0.085 A

V1 = I1 R1 = 0.085 x 15 = 1.28 V

V4 = I4 R4 = 1.11 V

V2 = V3 = 3 - 1.28 - 1.11 = 0.61 V

I2 = 0.61 / 10 = 0.061 A

I3 = 0.61/25 = 0.024 A

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