Question

Which one of the following is the correct equation for the electric circuit shown in the figure?

Options

• E₁ − (i₁ + i₂)R + i₁r₁ = 0

• E₁ − (i₁ + i₂)R − i₁r₁ = 0

• E₂ − i₂r₂ − E₁ − i₁r₁ = 0

• E₂ − (i₁ + i₂)R + i₂r₂ = 0

Answer 1

E₁ − (i₁ + i₂)R − i₁r₁ = 0

Explanation:

The current through the top resistor R is the sum of currents i₁ + i₂ (by junction rule).

Applying Kirchhoff’s Voltage Law (KVL) in the loop containing E₁, R, and r₁:

E₁ ​= (i₁​ + i₂​)R + i₁​r₁​

Rearranging:

E₁​ − (i₁​ + i₂​)R − i₁​r₁​ = 0