Question

The resistance of a resistor is reduced to half of its initial value. In doing
so, if other parameters of the circuit remain unchanged, the heating
effects in the resistor will become
(A)
two times.
(B)
half.
(C)
one-fourth.
(D)
four times.​

Answer 1

Answer:

A) two times

Reason- We know resistance is inversely proportional to the area of cross section of a wire.

Explanation:

Answer 2

The heating effects in the resistor will become two times.

• The resistance is given by :

        $V = IR$     where V is the voltage and I is the current.

• The voltage in the circuit remains unchanged. Hence the current will be given by :

        $I = \frac{V}{R}$     ....(1)

• This shows that when resistance increases , current decreases.

• The heating effect due to resistance is given by,

        $H = I^{2} R t$

• From equation (1)

        $H = \frac{V^{2} }{R} t$

• This shows that H is inversely proportional to R.

• $\frac{H1}{H2} = \frac{R2}{R1}$

        $H2 = \frac{R1}{0.5 R1} H1$

        $H2 = 2 H1$

• So, when the resistance is reduced to half the initial value, the heating effect in the resistor will become two times.  
• Option (A) is the right answer.