In the circuit, R=30.0 k Ωand C=0.10 μF. The capacitor is allowed to charge fully, and then the

step 1 Okay, we have a circuit in which we have a resistor that is 30 times 10 to the 3 oms. We have a

In the circuit, R=30.0 k Ωand C=0.10 μF. The capacitor is...

In the circuit, $R=30.0 \mathrm{k} \Omega$ and $C=0.10 \mu \mathrm{F}$. The capacitor is allowed to charge fully, and then the switch is changed from position $a$ to position $b$ What will the voltage across the resistor be $8.4 \mathrm{ms}$ later?

Key Concepts

Exponential Decay

Exponential decay describes how the voltage or charge in an RC circuit decreases over time when the capacitor discharges. The voltage across the capacitor (or related voltage across a resistor in series) typically follows an exponential function, decreasing as V(t) = V? exp(?t/?). This concept is key to understanding transient behaviors in circuits.

Transient Analysis

Transient analysis is the study of a circuit's response to a sudden change in its configuration, such as switching events. In RC circuits, this involves analyzing how voltages and currents change over time as the circuit moves from one equilibrium state to another, typically governed by the exponential functions derived from the time constant.

RC Circuits

RC circuits involve a resistor and a capacitor connected together, where the capacitor’s charging and discharging behavior is influenced by the resistor. These circuits are fundamental in electronics for filtering, timing, and transient applications as they smooth or delay voltage changes.

Time Constant

The time constant (?) in an RC circuit is defined as the product of the resistance (R) and the capacitance (C). It characterizes the rate at which the capacitor charges or discharges—a larger ? implies a slower rate of change. It is crucial for predicting how quickly a circuit will respond to a change, such as switching states.

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