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What is the effect of increasing the resistance in an RC circuit on the time constant?
Increasing the resistance increases the time constant, slowing down the charging or discharging process.
What is the effect of increasing the capacitance in an RC circuit on the time constant?
Increasing the capacitance increases the time constant, slowing down the charging or discharging process.
What happens to the current in a discharging RC circuit as time increases?
The current decreases exponentially as the capacitor discharges.
What happens to the voltage across a capacitor as it charges in an RC circuit?
The voltage increases exponentially, approaching the source voltage.
What happens when a capacitor is fully charged in a DC circuit?
The capacitor acts as an open circuit, blocking further current flow.
How do you calculate the equivalent capacitance of capacitors in series?
Calculate the reciprocal of each capacitance, sum the reciprocals, and then take the reciprocal of the sum: $\frac{1}{C_{\text{eq, s}}} = \sum_{i} \frac{1}{C_i}$.
How do you calculate the equivalent capacitance of capacitors in parallel?
Sum the individual capacitances: $\C_{\text{eq, p}} = \sum_{i} C_i$.
Describe the process of a capacitor charging in an RC circuit.
Initially, the uncharged capacitor allows easy charge flow, acting like a wire. As it charges, the charge on the plates increases, the current decreases, and the stored electric potential energy increases, approaching steady-state asymptotically.
Describe the process of a capacitor discharging in an RC circuit.
Charge and stored energy decrease, and current decreases over time. After a time much greater than $\tau$, the circuit reaches a steady state.
What is the first step to solving a complex RC circuit problem?
Simplify the circuit by finding equivalent capacitances for series and parallel combinations.
Label the components in a simple RC discharging circuit diagram (Capacitor, Resistor).
1: Capacitor (C), 2: Resistor (R)
Label the components in a simple RC charging circuit diagram (Voltage source, Capacitor, Resistor).
1: Voltage source ($\mathcal{E}$), 2: Resistor (R), 3: Capacitor (C)