Two rectangular loops share a common resistor

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits

Problem

Two rectangular loops share a common

4\,\Omega

resistor. The left loop contains a

10\,\text{V}

battery and a

2\,\Omega

resistor in series. The right loop contains a

5\,\text{V}

battery (opposing the left battery) and a

3\,\Omega

resistor in series. Both batteries have negligible internal resistance. Assume clockwise currents

I_1

in the left loop and

I_2

in the right loop. What is the current through the

4\,\Omega

resistor and its direction? (a)

1.92\,\text{A}

from right loop to left loop (b)

0.77\,\text{A}

from left loop to right loop (c)

1.54\,\text{A}

from left loop to right loop (d)

1.54\,\text{A}

from right loop to left loop