A heater is designed to operate with a power of $1000 W$ in a $100 V$ line. It is connected in combination with a resistance of $10Ω$ and a resistance $R$ , to a $100 V$ mains as shown in figure. For the heater to operate at $62.5 W$ , the value of $R$ should be _____ $Ω$ .

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TestHub · Accepted Answer

R heater ​ = P V 2 ​ = 1000 ( 100 ) 2 ​ = 10Ω For heater P = R V 2 ​ ⇒ V = PR ​ ​ V = 62.5 × 10 ​ V = 25 v ​ ​ i 1 ​ = 10 75 ​ = 7.5 A , i H ​ = 10 25 ​ = 2.5 A . i R ​ = i 1 ​ − i H ​ = 5 V = IR R = 5 25 ​ = 5Ω ​

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