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Heat is produced at a rate given by H in a resistor when it is connected across a supply of voltage V. If now the resistance of the resistor is doubled and the supply voltage is made V/3 then the rate of production of heat in the resistor will be
  • a)
    H/18
  • b)
    H/9
  • c)
    6H
  • d)
    18H
Correct answer is option 'A'. Can you explain this answer?
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Heat is produced at a rate given by H in a resistor when it is connect...
Given:
- Heat produced in a resistor is given by H when it is connected across a supply of voltage V.
- The resistance of the resistor is doubled.
- The supply voltage is made V/3.

To find:
The rate of production of heat in the resistor.

Solution:
Let the initial resistance of the resistor be R and the initial voltage across it be V.

1. Relationship between heat produced, voltage, and resistance:
According to Ohm's Law, the current flowing through a resistor is given by:
I = V/R
The power dissipated in the resistor (rate of production of heat) can be calculated using:
P = VI
Substituting the value of current in the above equation, we get:
P = (V/R) * V
P = V^2/R

2. Doubling the resistance:
If the resistance is doubled, the new resistance becomes 2R.

3. Changing the supply voltage:
If the supply voltage is made V/3, the new voltage becomes V/3.

4. Calculating the new rate of production of heat:
Using the formula derived in step 1, we can find the new rate of production of heat:
P' = (V/3)^2/(2R)
P' = V^2/(36R)

Comparing the initial rate of production of heat (P = V^2/R) and the new rate of production of heat (P' = V^2/(36R)), we can observe that the new rate is 1/36 times the initial rate.

Therefore, the rate of production of heat in the resistor is H/36.

As per the options provided, the correct answer is option 'A' - H/18. However, this answer may be incorrect as it does not match the derived value of H/36.
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