My house and my tool shed are wired together in series across a 220 V source. Th

Question

My house and my tool shed are wired together in series across a 220 V source. The tool shed has a fixed resistance R_1 = 10 Ohm because we keep the shed lights on all the time. The house has a resistance R_2 that varies, depending on what appliances we are running. (a) What is the power delivered to the house when R_2 = 1 Ohm ? What is the power delivered to the house when R_2 = 100 Ohm ? (b) For what value of R_2 will the power delivered to the house be maximum? What is this maximum power, in Watts?

Explanation / Answer

here V = 220 volt R1 = 10 ohm

as we know that the power delivered to the resistance

P = I2R

so I = V / (R1 + R2)

I = 220 / (10 + R2)

(a) when R2 = 1 ohm

I = 220 / (10+1) = 20 Amp

then P = 202 x 1 = 400 watt Ans

when R2 = 100 ohm

I = 220 / (10+100) = 2 Amp

P = 22 x 100 = 400 watt Ans

(b) when R1 = R2 = 10 ohm

then the maximum power transferred to the resistor due to minimum resistance

I = 220 / (10+10) = 11 Amp

then the maximum power

Pmax = 112 x 10 = 1210 watt Ans

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