Question

Compare the power used in the 2 Ω resistor in each of the following circuits:

1. a 6 V battery in series with 1 Ω and 2 Ω resistors
2. a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Answer 1

(i) Potential difference, V = 6 V
1 Ω and 2 Ω resistors are connected in series. Therefore, equivalent resistance of the circuit is

R = R₁ + R₂

= 1 + 2

= 3 Ω
current flowing in the circuit I_s = `"V"/"R"`
= `6/3`

= 2 A

Since equal electric current flows through all the resistances connected in series,

Therefore, power consumed by a 2 Ω resistor P₁ = (I₁)²R

= (2)² × 2

= 8 W

(ii) Here V = 4 V, R₁ = 12 Ω

And R₂ = 2 Ω

∴ The current flowing through different resistances connected in parallel is different but the potential difference between the ends remains the same.

Therefore, power consumed by a 2 Ω resistor P₂ = `"V"^2/"R"`

= `(4 "V")^2/(2 Ω)`

= 8W

Therefore, the 2 Ω resistor will consume the same amount of electrical power in both cases.

i.e., P₁ = P₂