A 8.3 resistor and a 5.4 resistor are connected in series with an emf source. The potential difference across the 5.4 resistor is measured with a voltmeter to be 12 V. Find the potential difference across the emf source.

The potential difference across the source is 30.45 V.

Explanation:

In this setup we have a voltage divider, we were given the voltage difference on one of the resistors, we know that the difference pottential from the source in this case is the sum of the voltage in each individual resistor, so we can use the following equation to solve this problem:

V_resistor5.4 = (V_source) * (R_5.4) / (R_5.4+R_8.3)

V_source = (V_resistor5.4) * (R_5.4+R_8.3) / (R_5.4)

V_source = (12) * (5.4+8.3) / 5.4

V_source = (12) * (13.7) / 5.4 = 30.45 V

he potential difference across the source is 30.45 V.