resistances in parallel

Question

Two resistors of 6 Ω and 3 Ω are connected in parallel. What is the equivalent resistance?

RankGuru · Accepted Answer

1. **Parallel Rule**: When resistors are in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.
   - Formula: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$.
2. **Calculation**:
   - $\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{3}$
   - $\frac{1}{R_{eq}} = \frac{1+2}{6} = \frac{3}{6} = \frac{1}{2}$.
3. **Invert**: $R_{eq} = 2 	ext{ } \Omega$.
4. **Quick Formula**: For two resistors, $R_{eq} = \frac{R_1 R_2}{R_1 + R_2} = \frac{18}{9} = 2 	ext{ } \Omega$.
5. **Note**: The equivalent resistance is always smaller than the smallest branch resistance (6 or 3).

Rank Guru

resistances in parallel

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