Question

Two solenoids have identical geometrical construction but one is made of thick wire and the other of thin wire. Which of the following quantities are different for the two solenoids?
(a) self-inductance
(b) rate of Joule heating if the same current goes through them
(c) magnetic field energy if the same current goes through them
(d) time constant if one solenoid is connected to one battery and the other is connected to another battery.

Answer 1

Current Flow Effects Joule Heating

Explanation:

(b) rate of Joule heating if the same current goes through them

(d) time constant if one solenoid is connected to one battery and the other is connected to another battery

Since the solenoids are indistinguishable, their self-inductance will be the equivalent.  

Resistance of a wire is given by, R =$\rho \frac{l}{A}$

Where,

l = Length of the wire

A = Area of cross section of the wire

$\rho$ = Resistivity of the wire

Because $\rho$ and l are the same for both wires, the thick wire will have greater area of cross section and hence less resistance than the thin wire.

⇒$R_t_h_i_c_k <R_t_h_i_n$

⇒$R_t_h_i_c_k <R_t_h_i_n$

The time constant for a solenoid is given by

$\tau = \frac {L}{R}$

Therefore, $\tau _t_h_i_c_k = > \tau _t_h_i_n$

• Thus, time constants of the solenoids would be different if one solenoid is connected to one battery and the other is connected to another battery.

• Also, since the self-inductance of the solenoids is same & same current flows through them so the magnetic field energy given by $\frac {1}{2} Li^2$ will be same.

Power dissipated as heat, P = $i^2R$

i is the same for both solenoids

So, $P_t_h_i_c_k < P_t_h_i_n$

Because the resistance of the coils are different, the rate of Joule heating will be different for the coils if the same current goes through them.