EMF, Internal Resistance and Terminal Voltage

Represent the real cell as ε in series with r. Decide whether the cell is delivering or receiving current. Find total circuit resistance if an external resistor is given. Calculate current. Apply V = ε - Ir for discharge or V = ε + Ir for charging. Include volt and ohm units.

Draw a real cell as an ideal emf ε in series with internal resistance r, connected to an external resistance R. Label current direction, terminal points, terminal voltage V, and internal drop Ir.

Using V = ε + Ir for a discharging cell gives a terminal voltage greater than the emf, which contradicts energy loss inside the cell.

EMF of a cell is the work done by the source per unit charge in driving charge around the complete circuit. Internal resistance is the opposition to current within the cell, and terminal voltage is the potential difference available across the cell terminals when current flows.

EMF of a cell is the work done by the source per unit charge in driving charge around the complete circuit. Internal resistance is the opposition to current within the cell, and terminal voltage is the potential difference available across the cell terminals when current flows. For a discharging cell: V = ε - Ir. For a charging cell: V = ε + Ir. Here V is terminal voltage in volt, ε is emf in volt, I is current in ampere, and r is internal resistance in ohm. For identical cells in series, emf adds and internal resistance adds. Conditions: use correct current direction and cell polarity. If a cell of emf 2.0 V and internal resistance 0.5 ohm supplies 1.0 A, its terminal voltage is 2.0 - 0.5 = 1.5 V.

A real cell is not an ideal source. It has internal resistance r, so some energy per unit charge is lost inside the cell when current flows. During discharge, terminal voltage V is less than emf ε and is given by V = ε - Ir. During charging, terminal voltage can exceed emf because the external source pushes current into the cell. This distinction is important in practical circuits and numerical problems involving cells. For a discharging cell: V = ε - Ir. For a charging cell: V = ε + Ir. Here V is terminal voltage in volt, ε is emf in volt, I is current in ampere, and r is internal resistance in ohm. For identical cells in series, emf adds and internal resistance adds. Conditions: use correct current direction and cell polarity. A cell has ε = 12 V and r = 1.0 ohm. It supplies current to an external resistance R = 5.0 ohm. Total resistance = R + r = 6.0 ohm, so I = ε/(R + r) = 12/6 = 2.0 A. Terminal voltage V = ε - Ir = 12 - 2 x 1 = 10 V. The external resistor receives 10 V, not the full emf. Exams ask for terminal voltage during discharge, current supplied by a cell with internal resistance, comparison of cells in series or parallel, and reasoning why terminal voltage changes with current. Using V = ε + Ir for a discharging cell gives a terminal voltage greater than the emf, which contradicts energy loss inside the cell.