A heater is designed to operate with a power of 1000 walts in a 100 volt line. It is connected in a combinations with a resistance of 10 ohms and a resistance R to a 100 volts mains as shown in figure. What should be the value of R so that the heater operates with a power of 62.5 watts.
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Explanation

Resistance of heater,
`R' = V^(2)/P = 100^(2)/1000 = 10 Omega`
When heater is in the circuit, let pot.diff. across heater be V, then `62.5 = V^(2)//10 or V^(2) = 625`
or V = 25 volt
Therefore, current through heater,
`I_(2) = V//R' = 25//10 = 2.5A`
Voltage drop across `10 Omega` resistor connected in series with heater ` = 100 -25 = 75` volt.
Main current `= 75/10 = 7.5 A`
`:.` Current through resistance `R = 7.5 - 2.5 = 5A`.
`:.` Resistance, `R = 25/2 = 5 Omega`