A circuit consists of a resistor of 1 ohm in series with a parallel arrangement of resistors of 12 ohm and 6 ohm. Calculate the total resistance of the circuit. Draw a diagram of the arrangement.

Below diagram shows the arrangement of resistors:

In the circuit, there are two parts. In the first part, two resistors of 6 Ω and 12 Ω are connected in parallel. If the equivalent resistance is R_p then

$\dfrac{1}{R$P} = \dfrac{1}{12} + \dfrac{1}{6} \\[0.5em] \dfrac{1}{RP} = \dfrac{1+2}{12} = \dfrac{3}{12} = \dfrac{1}{4} \\[0.5em] \Rightarrow R_P = 4 Ω

Hence, R_P = 4 Ω

In the second part, 1 Ω and (R_P = 4 Ω) are connected in series. If the equivalent resistance is R_s then

R_s = 1 + R_P = 1 + 4 = 5 Ω

Hence, total resistance of the circuit = 5 Ω