Correct Answer - Option 2 : 20 ohm
CONCEPT:
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Power: The rate of work done by electric energy is called power. It is denoted by P.
- The SI unit of power is the watt (W).
\(⇒P = \frac{W}{t} = VI = I^{2}R = \frac{V^{2}}{R}\)
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Watt is a small unit that's why kilowatt-hour is used as the unit for electrical energy.
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1 unit of electric energy: When a one-kilowatt load works for 1 hour then the energy consumed is called 1 unit of electricity.
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1 Unit of electricity = 1 KWh = 1000 Watt-hour = 3.6 × 106 J
- 1 Kilo-watt = 1000 Watt
- Work done (W) = Energy consumed = Heat (H) = Power (P) × Time taken (t)
CALCULATION:
- The rating of the heater is given i.e. P = 1000 W, V = 200 V
- From the above formula, the resistance of heater Rh can be calculated as
\(⇒R_{h} = \frac{V^{2}}{P} = \frac{200\times 200}{1000} = 40Ω \)
- Current through the heater is calculated as
\(⇒I = \frac{V}{R_{h}} = \frac{200}{40} = 5A\)
- For the same power dissipation, the current through the heater must be 5 A.
- When the heater is connected to a 400 V supply, the safe resistance of the circuit should be
\(⇒R_{h}+R = \frac{400}{5} = 40 Ω\)
⇒ R = 20 Ω
- Therefore the value of resistance R required to put in series with heater is 20Ω. Hence, the correct option is (4).
