A very long circuit

Electricity and Magnetism Level 4

A large number of AA batteries with emf \(\mathcal{E}=1.5~\mbox{V} \) and resistors with resistance \(R\) form an infinite circuit as shown in the figure. The internal resistance of the batteries is \(r\). Thevenin's theorem tells us that this infinite circuit can be replaced by a single source with emf \(\mathcal{E}_{eq}\), connected in series with an equivalent resistor \(R_{eq}\). Determine the equivalent emf \(\mathcal{E}_{eq}\) in volts if \(\frac{r}{R}=\frac{1}{2}.\)

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