# 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 \(\frac{r}{R}=\frac{1}{2}.\)

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.