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 it connected to one battery and the other is connected to another battery

Answer 1

Answer: (B), (D)

The correct options are
B Rate of Joule heating if the same current goes through them
D Time constant if one solenoid it connected to one battery and the other is connected to another battery

The inductance of the two solenoid will remain the same. $(L=\mu N^2(hollowarea\left)/lenght\right)$
the resistance of the two solenoid will differ. $(R=\rho lenght/(areaofconductor)$
Rate of joule heating $\left(i^{2}R\right)$ will differ if same current flows because resistance will differ.
magnetic field energy $\left(\frac{1}{2}L{i}^2\right)$ will remain same if same current flows because the inductance is same.
time constant$\left(L/R\right)$ will differ.