Question

An inductance L, resistance R, and ideal battery of emf ε are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t the current I is given by:

a.A
b.B
c.C
d.D
e.E

Answer 1

An RL circuit demonstrates exponential behavior of current when a series circuit with an inductor and a resistor is switched on and off. Current increases and approaches a maximum value when the circuit is closed and decreases according to an exponential decay when opened.

Step-by-step explanation:

The question pertains to an RL circuit and the behavior of current in such a circuit when it is switched on and off. When the switch is moved to position 1, the circuit is closed, and the current starts at zero and grows exponentially until it reaches a final value of I0 = ε/R, where R is the total resistance in the circuit. This behavior can be described by the equation I(t) = I0(1 - e-t/τ), where e is the base of the natural logarithm and τ (tau) is the time constant of the circuit given by L/R. When the switch is moved to position 2, current decreases exponentially due to the inductor opposing the change in current and energy loss in the resistor, following the equation I(t) = I0e-t/τ.