Resistance Parallel

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Two resistors 6 Ω and 3 Ω in parallel. Equivalent resistance?

RankGuru · Accepted Answer

1. **Parallel Connection**: When resistors are connected between the same two points, they are in parallel.
2. **Formula**: The reciprocal of the equivalent resistance is the sum of reciprocals of individual resistances:
   $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$
3. **Calculation**:
   - $\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6}$
4. **Solve for R**:
   - $R_{eq} = \frac{6}{3} = 2 	ext{ } \Omega$
5. **Shortcut**: For two resistors, $R_{eq} = \frac{R_1 R_2}{R_1 + R_2} = \frac{6 	imes 3}{6 + 3} = \frac{18}{9} = 2 	ext{ } \Omega$.

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Resistance Parallel

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