Find the emf E.?

Question

When switch S in the figure is open, the voltmeter V of the battery reads 3.07 V . When the switch is closed, the voltmeter reading drops to 2.96 V , and the ammeter A reads 1.67 A . Assume that the two meters are ideal, so they do not affect the circuit.

Answer 1

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3.07 volts IS the emf voltage of the battery.

perhaps you mean resistor r, as that is the only unknown.

voltage across it is 3.07–2.96 = 0.11 volts

r = R/I = 0.11 / 1.67 = 0.066 Ω

Answer 2

When there is no current flow, emf E is 3.07 V.