Physics / Unit 9: Electricity and Circuits
9.6 Parallel Circuits
Notes
In a parallel circuit, each part is on its own branch connected across the same two points.
- The voltage is the same across every branch.
- The branch currents add up to the total current.
- Total resistance: $\displaystyle \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$. It is always less than the smallest branch resistance.
- If one branch breaks, the others keep working. Homes are wired in parallel.
- Example: $6 \text{ } \Omega$ and $3 \text{ } \Omega$ in parallel: $\displaystyle \frac{1}{R} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6}$, so $R = 2 \text{ } \Omega$.
Practice
Two $10 \text{ } \Omega$ resistors are connected in parallel. What is the total resistance?
$\displaystyle \frac{1}{R} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10}$, so $R = 5 \text{ } \Omega$.
A $6 \text{ } \Omega$ and a $3 \text{ } \Omega$ resistor are in parallel across 12 V. What is the current through the $3 \text{ } \Omega$ resistor?
Each branch has the full 12 V: $\displaystyle I = \frac{12}{3} = 4 \text{ A}$.
Why are the lights in a house wired in parallel rather than in series?
Parallel branches share the same voltage and work independently.
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