$17$ . In the circuit shown above, the emf's of the batteries are given, as well as the currents in the outside and the resistance in the middle branch. What is the magnitude of the potential difference between $X$ $\newline$ (A) $4 \mathrm{~V}$ $\newline$ (B) $8 \mathrm{~V}$ $\newline$ (C) $10 \mathrm{~V}$ $\newline$ (D) $12 \mathrm{~V}$ $\newline$ (E) $16 \mathrm{~V}$

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17

. In the circuit shown above, the emf's of the batteries are given, as well as the currents in the outside and the resistance in the middle branch. What is the magnitude of the potential difference between

X

\newline

(A)

4 \mathrm{~V}

\newline

(B)

8 \mathrm{~V}

\newline

(C)

10 \mathrm{~V}

\newline

(D)

12 \mathrm{~V}

\newline

(E)

16 \mathrm{~V}

Identify Total Resistance: Identify the total resistance in the circuit. $\newline$ Since the resistance in the middle branch is given, we'll call it $R$ .
Apply Ohm's Law: Apply Ohm's Law to find the potential difference across the resistor. $V = IR$ , where $I$ is the current through the resistor and $V$ is the potential difference.
Determine Current: Determine the current through the resistor. The problem states the currents in the outside branches, but we need the current in the middle branch.
Use Kirchhoff's Law: Use Kirchhoff's current law to find the current in the middle branch. The sum of currents entering a junction equals the sum of currents leaving.
Calculate Potential Difference: Calculate the potential difference using the current found and the resistance. $\newline$ $V = IR$ .