# Internal resistance and a resistor as a potential divider

Based on the fact that batteries have some kind of internal resistance, if I had a circuit that consisted of a battery and a resistor of some kind would they act like a potential (voltage) divider?

Also does it need to have an output to be classified as a potential (voltage) divider?

• Yes on the first question - no on the second. But the reason that voltage dividers are useful is because you can adjust the voltage across the resistor by changing its value appropriately and then apply that voltage to some other circuit. – NickD May 18 '18 at 12:55

## 1 Answer

The Thevenin equivalent circuit of a battery is an ideal voltage source $V_B$ in series with a resistor $R_i$ representing the internal resistance of the battery. When you connect the battery to an external resistance $R$, a current $$I=\frac {V_B}{R_i+R}$$ will flow and the voltage drop over the resistance $R$ will be given by the voltage division $$V_R=V_B \frac {R}{R_i+R}$$