Question

A set of three coils having resistances 10 Ω, 12 Ω, and 15 Ω are connected in parallel. This combination is connected in series with a series combination of three coils of the same resistances. Calculate the total resistance and current through the circuit, if a battery of emf 4.1 Volt is used for drawing current.

Answer 1

In the following figure shows the electrical network. For resistances, 10 Ω, 12 Ω and 15 Ω connected in parallel the equivalent resistance (RP) is given by,

`1/"R"_"p" = 1/10 + 1/12 + 1/15`

`= (6 + 5 + 4)/60`

`= 15/60 = 1/4`

∴ R_p = 4 Ω

For resistance R_p , 10 Ω, 12 Ω and 15 Ω connected in series, the equivalent resistance,

R_s = 4 + 10 + 12 + 15 = 41 Ω

 Thus, the total resistance = R_s = 41 Ω

Now, V = lR_s

∴ 4.1 = I × 41

∴ I = 0.1 A

The total resistance and current through the circuit are 41 Ω and 0.1 A respectively.