Question

Find the currents i₁ and i₂ whose relations in an electric circuit are given as: 

4i₁ – 3i₂ = 1; 3i₁ – 5i₂ = 2
1. \({i_1} = - \frac{5}{{11}}\) and \({i_2} = - \frac{1}{{11}}\)
2. ​​\({i_1} = \frac{1}{{11}}\) ​and ​\({i_2} = \frac{5}{{11}}\)​
3. \({i_1} = - \frac{1}{{11}}\) and \({i_2} = - \frac{5}{{11}}\)
4. \({i_1} = \frac{5}{{11}}\) and \({i_1} = \frac{1}{{11}}\)

Answer 1

Correct Answer - Option 3 : \({i_1} = - \frac{1}{{11}}\) and \({i_2} = - \frac{5}{{11}}\)

Given equations are:

4i₁ – 3i₂ = 1 ⇒ 12i₁ – 9i₂ = 3

3i₁ – 5i₂ = 2 ⇒ 12i₁ – 20i₂ = 8

From the above two equations,

11i₂ = -5

⇒ i₂ = -5/11

⇒ i₁ = -1/11