Three 3ω resistance are connected in parallel what is the equivalent resistance?

Analysis

The question asks for the equivalent resistance of three resistors, each with a value of $3\Omega$, connected in a parallel circuit.

Concept

When resistors are connected in parallel, the reciprocal of the equivalent resistance ($R_{eq}$) is equal to the sum of the reciprocals of the individual resistances. The formula is:

Alternatively, for $n$ identical resistors of value $R$ connected in parallel, you can use the simplified formula:

Solution

Given:

• Resistance of each resistor ($R$) = $3\Omega$
• Number of resistors ($n$) = $3$

Using the standard formula:

Using the simplified formula:

The calculation confirms that the equivalent resistance is $1\Omega$.

Exam Tip

In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistor in the circuit. If you ever calculate a value larger than your individual resistors, you know you have made a mistake! Also, remember the "shortcut": if all resistors are identical, just divide the value of one resistor by the total number of resistors.