JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Current Electricity

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A resistor develops 500 J of thermal energy in 20 s when a current of 1.5 A is passed through it. If the current is increased from 1.5 A to 3 A , what will be the energy developed in 20 s .

(A)2000 J✓ Correct
(B)500 J
(C)1000 J
(D)1500 J

Answer: (A)

Solution

For a fixed resistance carrying a steady current for a fixed time, the heat developed is

E = I^{2} R t

, so it grows as the square of the current. Raising the current from

1.5 A

3 A

doubles it, and

\frac{E _{2}}{E _{1}} = (\frac{3}{1.5})^{2} = 4 \Rightarrow E_{2} = 4 \times 500 = 2000 J

In the same

20 s

the resistor now develops

2000 J

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Single correct option

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