Rectangular coil of area A , number of turns n , carrying current I , ...
Torque on a coil can be calculated using the equation:
τ = nABIsinθ
where,
τ is the torque on the coil,
n is the number of turns,
A is the area of the coil,
B is the magnetic field,
I is the current flowing through the coil,
θ is the angle between the normal to the coil and the magnetic field.
If the torque on the coil is doubled, it means that the new torque is 2τ. Let's analyze the effect on each parameter in the equation.
Effect on Number of Turns (n):
The number of turns, n, does not affect the torque directly. Therefore, doubling the torque does not have any effect on the number of turns.
Effect on Area of the Coil (A):
From the equation, τ = nABIsinθ, we can see that torque is directly proportional to the area of the coil, A. If the torque is doubled, it means that the new torque is 2τ. To keep the equation balanced, the area of the coil, A, must also be doubled. Therefore, option C, "only A is doubled," is correct.
Effect on Current (I):
From the equation, τ = nABIsinθ, we can see that torque is directly proportional to the current, I. If the torque is doubled, it means that the new torque is 2τ. To keep the equation balanced, the current flowing through the coil, I, must also be doubled. Therefore, option B, "both A and I are doubled," is incorrect.
Effect on Magnetic Field (B):
From the equation, τ = nABIsinθ, we can see that torque is directly proportional to the magnetic field, B. If the torque is doubled, it means that the new torque is 2τ. To keep the equation balanced, the magnetic field, B, must also be doubled. Therefore, option A, "both A and B are doubled," is incorrect.
Conclusion:
When the torque on a rectangular coil is doubled, only the area of the coil, A, is doubled. The number of turns, n, current, I, and magnetic field, B, do not change. Therefore, option C, "only A is doubled," is the correct option.