Two solenoids have identical geometrical cons | vedclass

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(A) The self-inductance of a solenoid is given by $L = \frac{\mu_0 N^2 A}{\ell_s}$. Since the geometrical construction $(A, \ell_s)$ and the number of

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$b, d$

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(A) The self-inductance of a solenoid is given by $L = \frac{\mu_0 N^2 A}{\ell_s}$. Since the geometrical construction $(A, \ell_s)$ and the number of turns $(N)$ are identical,the self-inductance $L$ is the same for both.The resistance of a wire is given by $R = \frac{ho \ell_w}{a}$,where $a$ is the cross-sectional area of the wire. Since the wires have different thicknesses,their cross-sectional areas $a$ are different,so their resistances $R$ are different.$(a)$ Self-inductance: Same.$(b)$ Rate of Joule heating $(P = I^2 R)$: Since $R$ is different,the rate of heating is different for the same current $I$.$(c)$ Magnetic potential energy $(U = \frac{1}{2} L I^2)$: Since $L$ is the same and $I$ is the same,the energy is the same.$(d)$ Time constant $(	au = \frac{L}{R})$: Since $L$ is the same but $R$ is different,the time constant is different.Therefore,quantities $(b)$ and $(d)$ are different.

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