Final answer:
The initial current in an RL circuit is zero when the switch is closed due to the inductor's opposition to change in current. The time constant of the circuit is 1.5 msec, which is not the time it takes to reach full current but is a factor in determining how quickly it approaches the steady state. Eventually, the voltage across the inductor is zero and the voltage across the resistor equals the supply voltage.
Step-by-step explanation:
The question relates to an RL circuit consisting of a direct current (DC) voltage source, a switch, a resistor, and an inductor. When the switch in the circuit is closed, the student is asking if the current is zero 1.5 milliseconds (msec) later.
Initially, when the switch is closed, the current in the circuit is zero because the inductor opposes any change in current. As time progresses, the current through the resistor increases until it reaches a steady state, where it is limited by the resistance of the circuit. The time it takes for the current to reach a certain fraction of its final value is determined by the time constant (τ) of the circuit, which is the product of the inductance (L) and the resistance (R). For this circuit, τ = L/R = (15 mH) / (10 Ω) = 1.5 msec. But this is the time constant, not the time to reach full current, which actually takes multiple time constants.
The eventual steady state current is calculated using Ohm's Law as I = V/R = 50 V / 10 Ω = 5 A. The voltage across the inductor in a DC steady state is zero because it only resists changes in current. The voltage across the resistor is equal to the supply voltage since there is no longer a change in current, and thus no voltage drop across the inductor.