 # Combination of Resistors-Series and Parallel

• Rseries = R1 + R2 + R3 + …….
• When 'n' identical resistances are connected Rseries = nR.
• When resistances are connected in series V1 : V2 : V3 = R1 : R2 : R3.
• When resistances are connected in series V = V1 + V2 + V3.
• In parallel combination potential is constant across the ends of resistances.
• In parallel combination i1 : i2 : i3 = \tt \frac{1}{R_{1}} : \frac{1}{R_{2}} : \frac{1}{R_{3}}
• In parallel combination i = i1 + i2 + i3.
• 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

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1. The equivalent resistance of the combination of resistors is
Rs = R1 + R2 + R3

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 Req = 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]