DC Sources of Electricity
DC sources questions test cells, batteries, internal resistance, and connection arrangements. You must distinguish primary from secondary cells, calculate terminal voltage under load, and handle capacity and charging limits.
Core rules
- A primary cell is not rechargeable; a secondary cell is rechargeable.
- Lead-acid nominal cell voltage is about 2.1 V; a 12 V battery has six cells in series.
- Internal resistance causes terminal voltage to fall as load current rises: V_terminal = EMF − I × r_internal.
- Series connection adds voltages while capacity stays the same; parallel connection adds capacity and current capability while voltage stays the same.
- Capacity in ampere-hours (Ah) is current × time; it is not energy. Energy also needs voltage.
- Charging requires a voltage above the battery EMF and current limited to the manufacturer's rate.
Worked example
A 12 V battery with 0.5 Ω internal resistance supplies a 5.5 Ω load. Find current and terminal voltage. Total resistance = 0.5 + 5.5 = 6.0 Ω. I = 12 / 6.0 = 2.0 A. Terminal voltage = 12 − (2.0 × 0.5) = 11 V. Reasoning: the internal resistance is in series with the load, so it reduces the voltage available at the terminals.
Traps
- Treating Ah as energy; Ah must be multiplied by voltage for watt-hours.
- Assuming series connection increases capacity; it increases voltage only.
- Forgetting internal resistance when calculating terminal voltage.
- Charging a non-rechargeable primary cell.