Question

A battery of e.m.f 16 V and internal resistance 2 Ω is connected to two resistors 3Ω and 6Ω connected in parallel. Find:

1. the current through the battery.
2. p.d. between the terminals of the battery,
3. the current in 3 Ω resistors,
4. the current in 6 Ω resistor. 

Answer 1

E.m.f. of battery E = 16V, r = 2Ω

Effective resistance of 3Ω and 6Ω connected in parallel R is

`1/"R" = 1/3 + 1/6`

= `3/6`

= `1/2`

∴ R = 2Ω

Total resistance = (R + r)

= (2 +2)

= 4Ω

(a) Current through battery
I = `"V"/("R" + r) = "E"/("R" +r)`

I = `(16V)/(4Ω)`

= 4 A

(b) p.d between terminal of battery

V = IR

= 4 × 2

= 8V

(c) The current in 3Ω resistor

I₁ = `"V"/"R"`

= `8/3`

= 2.66 A

(d) The current in 6Ω resistor 

I₂ = `"V"/"R"`

= `8/6`

= 1.34 A