Case: Read the following passage and answer accordingly.
The current through a single resistor R across which there is a potential difference V is given by Ohm’s law \( I=V/R \). Resistors are sometimes joined together and there are simple rules for the calculation of equivalent resistance of such a combination. Two resistors are said to be in series if only one of their endpoints is joined. Two or more resistors are said to be in parallel if one end of all the resistors is joined together and similarly the other ends joined together.
A current of 18 A divides between two branches in parallel of resistance \( 8\,\Omega \) and \( 12\,\Omega \) respectively. What is the current in each branch?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10.8 A, 7.2 A
Resistors in parallel have the same potential difference across them, so \( I_1R_1=I_2R_2 \). The total current divides in inverse ratio of the resistances, and the smaller resistance carries the larger current.
\( \begin{aligned} I_1 &= I\,\frac{R_2}{R_1+R_2} \\ &= 18\,\mathrm{A}\times\frac{12\,\Omega}{8\,\Omega+12\,\Omega} \\ &= 10.8\,\mathrm{A} \end{aligned} \)
\( \begin{aligned} I_2 &= I\,\frac{R_1}{R_1+R_2} \\ &= 18\,\mathrm{A}\times\frac{8\,\Omega}{8\,\Omega+12\,\Omega} \\ &= 7.2\,\mathrm{A} \end{aligned} \)
So the \( 8\,\Omega \) branch carries 10.8 A and the \( 12\,\Omega \) branch carries 7.2 A, which add up to 18 A.