Suppose four batteries are connected in series as shown...

Suppose four batteries are connected in series as shown below. (a) What is the equivalent emf of the set of four batteries? Treat them as ideal sources of emf.
(b) If the current in the circuit is $0.40 \mathrm{A},$ what is the value of the resistor $R ?$

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Key Concepts

Series Connection of Voltage Sources

In a series circuit, multiple voltage sources (such as batteries) are connected end-to-end, so their individual electromotive forces (emfs) add up to form the equivalent or total emf of the series. This concept is used to predict how the voltage across the entire arrangement will compare to the voltage of a single source.

Electromotive Force (EMF)

Electromotive force (emf) represents the voltage generated by a battery or other energy source when no current is flowing. In circuit analysis, emf is a fundamental parameter used to determine the potential difference that drives current through the circuit.

Ohm's Law

Ohm's Law is a key principle in circuit analysis which states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is mathematically expressed as V = IR, and it is instrumental in determining unknown quantities in a circuit when two of the three variables (voltage, current, resistance) are known.

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