A solenoid having an inductance of 6.30 μH is connected in series with a 1.20 k Ωresistor. (a) I

step 1 In the given RL series circuit value of inductance is given as 6 .30 micro henry and resistance

A solenoid having an inductance of 6.30 μH is connected in...

A solenoid having an inductance of $6.30 \mu \mathrm{H}$ is connected in series with a $1.20 \mathrm{k} \Omega$ resistor. (a) If a $14.0 \mathrm{~V}$ battery is inserted into the circuit, how long will it take for the current through the resistor to reach $80.0 \%$ of its final value? (b) What is the current through the resistor at time $t=1.0 \tau_{l} ?$

Key Concepts

RL Circuit

An RL circuit is an electrical circuit consisting of resistors and inductors driven by a voltage source. It is used to study how inductance, which resists changes in current, interacts with resistance to affect the time-dependent behavior of circuit current during transient and steady-state states.

Time Constant

The time constant in an RL circuit, defined as the ratio of inductance to resistance (? = L/R), characterizes the rate at which the current changes in response to a sudden change in applied voltage. It indicates how quickly the circuit approaches its steady-state value after being energized.

Exponential Transient Response

During the transient period immediately after the application of a voltage, the current in an RL circuit grows according to an exponential function, typically expressed as I(t) = I_final(1 - exp(-t/?)). This behavior describes how the current gradually increases from zero to its final steady-state value over time.

Steady-State Current

The steady-state current in an RL circuit is the final, constant current achieved after all transient effects have decayed. It is determined by Ohm’s Law (I = V/R) when the inductor behaves as a short circuit in the long term, meaning the current is only limited by the resistor.

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