The effective resistance between P and Q of the electrical circuit shown in the figure is

Question

The effective resistance between P and Q of the electrical circuit shown in the figure is (A) (5R /2) + 2r (B) 8R (R + r)/(3R + r) (C) 2Rr/(R+r) (D) 2 r + 4R

Tardigrade Admin · Accepted Answer

Equivalent circuits of given circuit are shown.

\frac{1}{R ^{'}} = \frac{1}{2 R} + \frac{1}{r} + \frac{1}{2 R} ∴ R^{'} = \frac{R r}{R + r}

Total resistant

R^{''} = R^{'} + R^{'} = \frac{2 R r}{R + r}

Q. The effective resistance between $P$ and $Q$ of the electrical circuit shown in the figure is

$(5 R /2) + 2 r$

$8 R (R + r) / (3 R + r)$

$2 R r / (R + r)$

$2 r + 4 R$

Equivalent circuits of given circuit are shown.

$\frac{1}{R ^{'}} = \frac{1}{2 R} + \frac{1}{r} + \frac{1}{2 R} ∴ R^{'} = \frac{R r}{R + r}$
Total resistant $R^{''} = R^{'} + R^{'} = \frac{2 R r}{R + r}$

Q. The effective resistance between P and Q of the electrical circuit shown in the figure is

(5R/2)+2r

8R(R+r)/(3R+r)

2Rr/(R+r)

2r+4R