Question

In two situations given in figures (i) and (ii) current through R is \(I_1\) and \(I_2\) respectively. If \(E_1 = 2\ V\), \(r_1 = 1 \Omega,\)\(E_2 = 1\ V , r_2= 2 \ \Omega, R = 6 \ \Omega\) then find \(\frac{I_1}{I_2}\) .

(1) \(\frac{3}{4}\)

(2) \(\frac{4}{3}\)

(3) \(\frac{9}{4}\)

(4) \(\frac{4}{9}\)

Answer 1

Correct option is: (2) \(\frac{4}{3}\)

\(I_1= \frac{E_{eq}}{r_1 + r_2 + R} = \frac{1}{3}\)

\(I_2= \frac{E_{eq}}{r_{eq} + R}\)

\(E_{eq} = \frac{\frac{E_1}{r_1} +\frac{E_2}{r_2}}{\frac{1}{r_1} + \frac{1}{r_2}} = \frac{5}{3}\)

\(i_2 = \frac{1}{4}\)

\(\frac{i_1}{i_2} = \frac{4}{3}\)