Question

(a) Three resistors 1 Ω, 2 Ω, and 3 Ω are combined in series. What is the total resistance of the combination?
(b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, obtain the potential drop across each resistor.

Answer 1

(a) Three resistors of resistances 1 Ω, 2 Ω, and 3 Ω are combined in series. Total resistance of the combination is given by the algebraic sum of individual resistances. Total resistance = 1 + 2 + 3 = 6 Ω

(b) Current flowing through the circuit = I
Emf of the battery, E = 12 V
Total resistance of the circuit, R = 6 Ω
The relation for current using Ohm’s law is,

Potential drop across 1 Ω resistor = V₁
From Ohm’s law, the value of V₁ can be obtained as V1 = 2 × 1= 2 V … (i)
Potential drop across 2 Ω resistor = V₂ 

Again, from Ohm’s law, the value of V₂ can be obtained as 

V₂ = 2 × 2= 4 V … (ii)
Potential drop across 3 Ω resistor = V₃ 

Again, from Ohm’s law, the value of V₃ can be obtained as
V₃ = 2 × 3= 6 V … (iii)
Therefore, the potential drop across 1 Ω, 2 Ω, and 3 Ω resistors are 2 V, 4 V, and 6 V respectively.