Question

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.

Answer 1

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

`1/"R"_"p" = 1/12 + 1/6`

`1/"R"_"p" = (1 + 2)/12`

`1/"R"_"p" = 3/12`

`1/"R"_"p" = 1/4` 

⇒ 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 

R_s = 1 + 4

R_s = 5 Ω