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 10 Ω and a resistance R to a 100V line as shown in figure. What should be the value of R so that the heater operates with a power of 62.5 W?
Question
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 10 Ω and a resistance R to a 100V line as shown in figure. What should be the value of R so that the heater operates with a power of 62.5 W?
Solution
The problem can be solved using the formula for power and Ohm's law.
Step 1: Calculate the resistance of the heater when it operates at 1000W.
The formula for power is P = V^2 / R. We can rearrange this to find R = V^2 / P.
Substituting the given values, we get R = (100V)^2 / 1000W = 10 Ω.
Step 2: Calculate the total resistance of the circuit when the heater operates at 62.5W.
Again using the formula for power, we get R = V^2 / P = (100V)^2 / 62.5W = 160 Ω.
Step 3: Calculate the value of R.
The total resistance of the circuit is the sum of the resistances of the heater, the 10 Ω resistor, and R.
So, 160 Ω = 10 Ω + 10 Ω + R.
Solving for R, we get R = 160 Ω - 20 Ω = 140 Ω.
So, the value of R should be 140 Ω for the heater to operate with a power of 62.5W.
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