Question

In a circuit with two (12 ohms and 4 ohms) resistors connected in parallel and a voltage of 12V, what proportion of the current will flow through the 12 ohms resistor

Answer 1

To find the proportion of the current flowing through the 12-ohm resistor in a parallel circuit with a 12-ohm and a 4-ohm resistor connected across a 12V supply, we can use Ohm's Law and the concept of parallel resistances.

1. **Calculate the total current (I_total)** supplied by the voltage source:
The equivalent resistance (R_eq) for resistors in parallel is given by the formula:

\[
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}
\]

where \( R_1 = 12 \, \Omega \) and \( R_2 = 4 \, \Omega \).

\[
\frac{1}{R_{eq}} = \frac{1}{12} + \frac{1}{4}
\]

Convert \( \frac{1}{4} \) to have a common denominator:

\[
\frac{1}{R_{eq}} = \frac{1}{12} + \frac{3}{12} = \frac{4}{12} = \frac{1}{3}
\]

Therefore:

\[
R_{eq} = 3 \, \Omega
\]

Now, using Ohm's Law:

\[
I_{total} = \frac{V}{R_{eq}} = \frac{12V}{3\Omega} = 4A
\]

2. **Calculate the current through each resistor**:
Now we can find the current through each resistor using Ohm's Law again.

For the 12-ohm resistor:

\[
I_{12\Omega} = \frac{V}{R_1} = \frac{12V}{12\Omega} = 1A
\]

For the 4-ohm resistor:

\[
I_{4\Omega} = \frac{V}{R_2} = \frac{12V}{4\Omega} = 3A
\]

3. **Proportion of the current through the 12-ohm resistor**:
The proportion of the total current that flows through the 12-ohm resistor is given by:

\[
\text{Proportion} = \frac{I_{12\Omega}}{I_{total}} = \frac{1A}{4A} = \frac{1}{4}
\]

Thus, the proportion of the current that flows through the 12-ohm resistor is \( \frac{1}{4} \) or 25%.