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A 7.1 resistor and a 4.8 resistor are connected in series with a battery. the potential difference across the 4.8 resistor is measured as 12 v. find the potential difference across the battery. v

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sqdancefan
For resistors in series in a DC circuit, the potential difference is proportional to the resistance.

The voltage V across the 7.1 ohm resistor can be found from the proportion
   V/7.1 = 12/4.8
   V = 7.1*12/4.8 = 17.75

The potential difference at the battery terminals is the sum of the potential differences across the two series resistors.
   Vbatt = 17.75 V + 12 V
   Vbatt = 29.75 V