Question

A battery o f e.m.f. 3 Vis connected in series with an ammeter, a 10 Ω coil of wire and with a parallel combination o f resistance of 3Ω and 6 Ω. Draw a circuit diagram for the above arrangement. What is the
(a) Resistance of the parallel combination?
(b) Reading on the ammeter?
( c) Potential difference across the 3Ω resistor?
( d) Current flowing through each resistor?

Answer 1

(a) Resistance of parallel combination:

`1/"R"_"parallel" = 1/3 + 1/6 = 3/6 = 1/2` Ω

`"R"_"parallel" = 2`Ω 

(b) Total resistance of the circuit =

`"R"_"total" = 2 + 10= 12`Ω 

Let I be the current through the ammeter, the:

I = `"V"/"R"_"total" = 3/12 = 1/4` = 0.25 A

(c) Potential drop across 10 0 resistor, V₁ = I x 10= 0.25 x 10 = 2.5V

:. Potential drop across 3Ω  resistor, V₂ = e - V₁ = 3 - 2.5 = 0.5V

(d) Current flowing through 10 Ω  resistor= 0.25 A

Current flowing through 3 Ω resistor = `"V"_2/"R" = 0.5/3` = 0.17 A

Current flowing through 6 Ω resistor= 0.25 · 0.17 = 0.08 A