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A conducting loop of finite resistance lies in the x-y plane. There is a constant magnetic field in the z direction. The area of the loop varies with time t as A=A₀(1+sin t) in appropriate units. The figure that correctly indicates the qualitative behaviour of the power P dissipated in the loop as a function of time is:

Asked in RE-NEET 2026 · Induced current, heat and power

• (1) P swings between positive and negative values, like cos t
• (2) P rises steadily with time
• (3) a train of identical positive humps that touch zero at t=π/2,(3π)/2,… and peak in between, of period π
• (4) a curve shaped like 1+sin t, never touching zero

Step-by-step solution

Why the other options are wrong

• (1) comes from cannot be: power dissipated in a resistance is I²R, which is never negative.
• (2) comes from would need the induced current to grow without limit, but it is periodic.
• (4) comes from follows the area rather than its rate of change, and never reaches zero as cos²t must.

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