Question

Solve the following problem.

Two resistors 1 kΩ and 2 kΩ are connected in parallel combination.

1. Find equivalent resistance of parallel combination
2. When this parallel combination is connected to 9 V supply, by neglecting internal resistance calculate current through each resistor.

Answer 1

Given: R₁ = 1 kΩ = 10³ Ω, R₂ = 2 kΩ = 2 × 10³ Ω, V = 9 V

To find: i. Parallel equivalent resistance (R_P)
ii. Current through 1 kΩ and 2 kΩ (I₁ and I₂)

Formula: i. `1/"R"_"p"=1/"R"_1+1/"R"_2`
ii. V = IR

Calculation: From formula (i),

`1/"R"_"p"=1/10^3+1/(2xx10^3)`

= `3/(2xx10^3)`

∴ R_p = `(2xx10^3)/3` = 0.66 kΩ

From formula (ii),

I₁ = `"V"/"R"_1=9/10^3`

= 9 × 10⁻³ A
= 9 mA

I₂ = `"V"/"R"_2=9/(2xx10^3)`

= 4.5 × 10⁻³ A
= 4.5 mA

1. The equivalent resistance of the parallel combination is 0.66 kΩ.
2. Current flowing through 1 kΩ and 2 kΩ resistances are 9 mA and 4.5 mA respectively.