The diagram shows a circuit with the key k open. Calculate:
the resistance of the circuit when the key k is open.
Topic: Current, resistance and circuits
Answer
With the key k open, the branch containing the key carries no current, so only the 5 Ω resistor is in the circuit.
external resistance = 5 Ω
The cell has an internal resistance r = 0.5 Ω, which is in series with the external resistance: total resistance = 5 + 0.5 = 5.5 Ω
Total resistance of the circuit = 5.5 Ω (the external resistance alone is 5 Ω).
An open key means an open gap: no current can flow through that branch at all, so every resistor on it is simply out of the circuit. Ignore them completely rather than trying to include them in a parallel calculation.
The cell's internal resistance is always in SERIES with whatever is outside, so it adds on at the end. Read the question wording closely — "resistance of the circuit" normally means the whole loop including r, while "external resistance" means only what is outside the cell.