## Current Electricity

# Combination of Resistors-Series and Parallel

- R
_{series}= R_{1}+ R_{2}+ R_{3}+ ……. - When 'n' identical resistances are connected R
_{series}= nR. - When resistances are connected in series V
_{1}: V_{2}: V_{3}= R_{1}: R_{2}: R_{3}. - When resistances are connected in series V = V
_{1}+ V_{2}+ V_{3}. - In parallel combination potential is constant across the ends of resistances.
- In parallel combination i
_{1}: i_{2}: i_{3}= \tt \frac{1}{R_{1}} : \frac{1}{R_{2}} : \frac{1}{R_{3}} - In parallel combination i = i
_{1}+ i_{2}+ i_{3}. - In parallel combination \tt \frac{1}{R_{Eff}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}
- When ‘n’ equal resistances are connected in parallel \tt R_{Eff} = \frac{R}{n}
- If ‘n’ wires each of resistance "R" are connected to form a closed polygon \tt R_{Eff} = \frac{(n-1)}{n} R.
- A resistance wire ‘R’ is in the form of a circle. The resistance across diametric ends. \tt R_{Eff} = \frac{R}{4}

- A wire bent in the form of a circle \tt R_{AB} = \frac{R \theta (2 \pi - \theta)}{4 \pi r^{2}}
- Resistance of a hollow cylinder \tt R = \frac{\rho \ l}{\pi \left(r_{1}^{2} - v_{2}^{2}\right)}
- 12 wires each of resistance "r" are connected in the form of cube. \tt R_{across \ diagonal = \frac{5r}{6}}
- \tt R_{face \ diagonal} = \frac{3r}{4}
- \tt R_{two \ adjacent \ corners} = \frac{7r}{12}

### View the Topic in this video From 17:34 To 54:14

1. The equivalent resistance of the combination of resistors is

R_{s} = R_{1} + R_{2} + R_{3}

2. The equivalent resistance of the combination of resistors is

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

3. If *n* identical resistances are connected in series *R _{eq}* =

*nR*and potential difference across each resistance is

*V*=

*V*/

*n*

4. Current through any resistance is

\tt i = I_{total} \times \left[\frac{Resistance \ of \ opposite \ branch}{Total \ resistance}\right]