Add the individual resistances: $R_{\text{eq}, s} = \sum_{i} R_{i}$

Use the reciprocal sum formula: $\frac{1}{R_{\text{eq}, p}} = \sum_{i} \frac{1}{R_{i}}$

Subtract the voltage drop across the internal resistance from the emf: $\Delta V_{\text{terminal}} = \mathcal{E} - Ir$

Series: Single path for current, current is the same through each resistor, resistances add directly. | Parallel: Multiple paths for current, voltage is the same across each resistor, reciprocal sum for equivalent resistance.

Ideal: Constant voltage, zero internal resistance. | Non-Ideal: Voltage drops with current, has internal resistance.

Ideal: Zero resistance, no impact on circuit. | Non-Ideal: Small resistance, decreases measured current.

Ideal: Infinite resistance, no current draw. | Non-Ideal: Finite resistance, draws some current, affecting voltage measurement.

Add the individual resistances: $R_{\text{eq}, s} = \sum_{i} R_{i}$

Use the reciprocal sum formula: $\frac{1}{R_{\text{eq}, p}} = \sum_{i} \frac{1}{R_{i}}$

Subtract the voltage drop across the internal resistance from the emf: $\Delta V_{\text{terminal}} = \mathcal{E} - Ir$