Question

i. Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What is the total resistance of the combination?

ii. If the combination is connected to a battery of e.m.f. 20 V and negligible internal resistance, determine the current through each resistor and the total current drawn from the battery.

Answer 1

Given: R₁ = 2Ω, R₂ = 4 Ω, R₃ = 5 Ω,

V = 20 V

To Find: i. Total resistance (R)

ii. Current through each resistor (I₁, I₂, I₃ respectively)

iii. Total current (I)

Formulae:

i. \(\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)

ii. V = IR

iii. Total current, I = I₁ + I₂ + I₃

Calculation:

From formula (i):

∴ R = \(\frac{20}{19}\) Ω

From formula (ii):

From formula (iii):

I = 10 + 5 + 4

∴ I = 19 A