Question

A 17.0 resistor and a 6.0 resistor are connected in series with a battery. The potential difference across the 6.0 resistor is measured as 15 V. Find the potential difference across the battery.

Answer 1

Answer:

V= 57.5 V

Explanation:

• If the resistors are in the linear zone of operation, the potential difference across them, must obey Ohm's law:

        $V = I*R$

• For the 6.0 Ω resistor, if the potential difference across it is 15 V, we can find the current flowing through it as follows:

       $I = \frac{V}{R} = \frac{15 V}{6.0 \Omega} = 2.5 A$

• In a series circuit, the current is the same at any point of it, so the current through the battery is I = 2.5 A
• The equivalent resistance of a series circuit is just the sum of the resistances, so, in this case, we can write the following equation:

      $R_{eq} = R_{1} +R_{2} = 17.0 \Omega + 6.0 \Omega = 23.0 \Omega$

• Applying Ohm's Law to the equivalent resistance, we can find the potential difference through it, that must be equal to the potential difference across the battery, as follows:

        $V = I* R_{eq} = 2.5 A * 23.0 \Omega = 57.5 V$