The switch in FIGURE P34.80 has been open for a long time....

The switch in FIGURE P34.80 has been open for a long time. It is closed at $t=0 \mathrm{s}$ a. After the switch has been closed for a long time, what is the current in the circuit? Call this current $I_{0}$. b. Find an expression for the current $I$ as a function of time. Write your expression in terms of $I_{0}, R,$ and $L$ c. Sketch a current-versus-time graph from $t=0$ s until the current is no longer changing.

The switch in FIGURE P34.80 has been open for a long time. It is closed at $t=0 \mathrm{s}$
a. After the switch has been closed for a long time, what is the current in the circuit? Call this current $I_{0}$.
b. Find an expression for the current $I$ as a function of time. Write your expression in terms of $I_{0}, R,$ and $L$
c. Sketch a current-versus-time graph from $t=0$ s until the current is no longer changing.

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Key Concepts

RL Circuit

An RL circuit is an electrical circuit that contains both a resistor (R) and an inductor (L). The inductor stores energy in its magnetic field and resists changes in current, which leads to time-dependent behavior following switching actions such as closing or opening a switch.

Time Constant (?)

The time constant in an RL circuit, defined as ? = L/R, quantifies the rate at which the circuit responds to a change. It indicates the characteristic time over which the current reaches about 63% of its final steady-state value after a switch is closed or opened.

Transient Response

The transient response describes how the current changes from its initial value to its final steady-state value immediately after the circuit is switched. In an RL circuit, the current increases gradually in an exponential manner rather than instantaneously due to the inductor’s opposition to rapid changes in current.

Steady-State Behavior

Steady-state behavior refers to the condition when all transient effects have died out and the current in the circuit becomes constant over time. In an RL circuit, the inductor eventually behaves like a short circuit, so the current stabilizes at its maximum value determined by the applied voltage and the resistance.

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