True or false on induction (2)

Problem

True or false? (a) The induced electromotive force depends on the rate of change of the flux, not on the flux itself. (b) Lenz’s law is a consequence of energy conservation. (c) In an ideal transformer the output power exceeds the input power. (d) In an RL circuit the current is established with characteristic time $\tau = L/R$. (e) Eddy currents produce unwanted dissipation in magnetic cores.

Solution

(a) True. From Faraday’s law $\mathcal{E} = -\ddt{\Phi_B}$: what matters is the derivative of the flux, not its instantaneous value.

(b) True. The direction of the induced current opposes the change: if it were the same direction, energy would be spontaneously produced, violating conservation.

(c) False. In an ideal transformer $P_{\text{out}} = P_{\text{in}}$; the output power can never exceed the input power (in real transformers it is lower, due to losses).

(d) True. The time constant of the RL transient is $\tau = \dfrac{L}{R}$.

(e) True. Eddy currents dissipate energy by the Joule effect in the cores; that’s why cores are built from insulated laminations.

Summary: $\ev{\text{T, T, F, T, T}}$.

Collegamenti

Argomenti: Electromagnetic induction Concetti: Faraday-Neumann-Lenz law · Lenz’s law · Eddy currents · Inductance and self-induction