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Question Number 41231 by tanmay.chaudhury50@gmail.com last updated on 03/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 03/Aug/18

$f i n d e q u i v a l a n t r e s i s t a n c e b e t w e e n p o i n t A a n d B$
	Answered by ajfour last updated on 03/Aug/18

	$V_{A} - i r - I R = V_{B}$ $\Rightarrow V_{A} - V_{B} = i r + I R . . . (i)$ $l e f t l o o p e q .$ $V_{A} - i r - (i - I) r + I R = V_{A}$ $\Rightarrow I (R + r) = 2 i r$ $o r \frac{I}{i} = \frac{2 r}{R + r} . . . . (i i)$ $R_{e q} = \frac{V_{A} - V_{B}}{i + I} . . . . (i i i)$ $u s i n g (i) & (i i) i n (i i i)$ $R_{e q} = \frac{i r + I R}{i + I} = \frac{r + \frac{I}{i} R}{1 + \frac{I}{i}}$ $R_{e q} = \frac{r + \frac{2 r R}{R + r}}{1 + \frac{2 r}{R + r}} = \frac{r (r + 3 R)}{R + 3 r} .$
	Commented by tanmay.chaudhury50@gmail.com last updated on 04/Aug/18

	$t h a n k y o u . . .$
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