It increases the time constant, slowing down the charging/discharging process.

It increases the time constant, slowing down the charging/discharging process.

The current decreases over time, approaching zero when the capacitor is fully charged.

The stored energy in the capacitor is dissipated as heat in the resistor, and the capacitor's voltage decreases.

Charge begins to flow, accumulating on the capacitor plates, and a current flows through the resistor.

Initially, the capacitor acts like a wire, allowing charge flow. As it charges, its potential difference increases, current decreases, and energy is stored until fully charged with zero current.

The capacitor releases stored charge through the resistor. Potential difference, current, and stored energy decrease over time until reaching steady state.

Sum the inverses of individual capacitances: $\frac{1}{C_{eq,s}} = \sum_{i} \frac{1}{C_i}$.

Simply add the individual capacitances: $C_{eq,p} = \sum_{i} C_i$.

Multiply the equivalent resistance and equivalent capacitance: $\tau = R_{eq}C_{eq}$.

1. Identify all capacitors in series. 2. Calculate the inverse of each capacitance. 3. Sum the inverses. 4. Take the inverse of the sum to find $C_{eq,s}$: $\frac{1}{C_{\text{eq}, \text{s}}}=\sum_{i} \frac{1}{C_{i}}$ .

1. Identify all capacitors in parallel. 2. Sum the individual capacitances to find $C_{eq,p}$: $C_{\text {eq.p }}=\sum_{i} C_{i}$.

1. Initially, the uncharged capacitor acts like a wire. 2. Charge flows, increasing the capacitor's potential difference and stored energy. 3. The rate of charging decreases over time. 4. After a long time, the capacitor is fully charged, and the current becomes zero.

1. Initially, the capacitor is charged. 2. Charge flows out of the capacitor through the resistor, decreasing its potential difference and stored energy. 3. The rate of discharging decreases over time. 4. After a long time, the capacitor is fully discharged, with zero charge and energy.

Multiply the equivalent resistance ($R_{eq}$) by the equivalent capacitance ($C_{eq}$): $\tau = R_{eq}C_{eq}$.