Question

In the given electrical circuit, which one of the following equations is a correct equation?

Options

• E₂ - i₂r₂ - E₁ - i₁r₁ = 0

• E₁ - (i₁ + i₂)R + i₁r₁ = 0

• E₁ - (i₁ + i₂)R - i₁r₁ = 0

• - E₂ - (i₁ + i₂)R + i₂r₂ = 0

Answer 1

E₁ - (i₁ + i₂)R - i₁r₁ = 0

Explanation:

The given circuit can be drawn as

Applying Kirchhoff's voltage law (KVL) in loop ABCDA, we get

- (i₁ + i₂)R + E₂ - i₂r₂ = 0    ...(i)

Applying KVL in loop ABFEA, we get

- (i₁ + i₂)R - i₁r₁ + E₁ = 0     ...(ii)

Applying KVL in loop EFCDE, we get

- E₁ + i₁r₁ + E₂ - i₂r₂ = 0     ...(iii)

From the given options, only 3rd option is satisfies Eq. (ii),

Hence it is the correct equation.