Question

The drawing shows three different resistors in two different circuits. The battery has a voltage of V = 20 V, and the resistors have resistances of R1 = 50.0 Ω, R2 = 25.0 Ω and R3 = 10.0 Ω. Determine the current through and the voltage across each resistor.

Answer 1

A)

Req = R1 + R2 +R3= 50 +25 + 10 = 85 ohm

Gotal current I = V/Req = 20/85 = 0.235 A

in the series circuit, the current through each resistor will be same, so

I1=I2 = I3 = I = 0.235 A

V1 = I1*R1 = 0.235 x 50 = 11.76 V

V2 = I2R2 = 0.235 x 25 = 5.88 V

V3 = I3R3 = 0.235 x 10 = 2.35 V

B)

Req =1/[(1/R1)+(1/R2)+(1/R3)] = 6.25 ohm

the total current I = V/Req = 20/6.25 = 3.2 A

in parallel circuit, are resistors have the same voltage,

V1 = V2=V3 = V = 20 V

I1 = V1/R1 = 20 /50 = 0.4 A

I2 = V2/R2 = 20/25 = 0.8 A

I3 = V3/R3 = 20/10 = 2 A

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Answer 2

SOLUTION :

1. In series :

Total Resistance = R1 + R2 + R3 = 50+25+10 = 85 Ω

Current I in the circuit = V / Total R = 20 / 85 = 0.235 Amp.

So, current through each resistance = 0.24 Amp. (ANSWER)

V1 across R1 = IR1 = 0.235*50 = 11.75 V (ANSWER)

V2 across R2 = IR2 = 0.235*25 = 5.87 V (ANSWER)

V3 across R3 = IR3 = 0.235 * 10 = 2.35 V  (ANSWER)

2.

In parallel :

Current through R1 = V/R1 = 20/50 = 0.40 Amp.  (ANSWER)

Current through R2 = V/R2 = 20/25 = 0.80 Amp. (ANSWER)

Current through R3 = V/R3 = 20/10 = 2.00 Amps  (ANSWER)

Voltage across each resistance = 20 V (ANSWER)