Resistance in series and parallel Circuit

Resistance in Series and Parallel Circuit

In a series circuit, the effective resistance is equal to the sum of the individual resistance, as shown in the following equation.

$R = R_{1} + R_{2} + R_{3}$
In a parallel circuit, the effective resistance of the resistors can be calculated fro the following equation.

$R = {(\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}})}^{- 1}$

Example:

Find the equivalent resistance of the connection shown in the diagram above
Answer:
(a)

R = 2 + 3 + 6 = 11 Ω

(b)

\begin{array}{l} R = {(\frac{1}{3} + \frac{1}{3} + \frac{1}{3})}^{- 1} = 1 Ω \\ o r \\ R = 3 Ω \div 3 = 1 Ω \end{array}

(c)

\begin{array}{l} R = {(\frac{1}{6} + \frac{1}{6})}^{- 1} = 3 Ω \\ R = 6 Ω \div 2 = 3 Ω \end{array}

(d)

R = 3 + {(\frac{1}{2} + \frac{1}{2})}^{- 1} = 4 Ω