JEE PYQ: Current Electricity Question 42
Question 42 - 2019 (09 Apr 2019 Shift 1)
A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD)
(1) $R$
(2) $\frac{7}{64}R$
(3) $\frac{3}{4}R$
(4) $\frac{1}{16}R$
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Answer: (2)
Solution
$R_{DA} = R_{AB} = R_{BC} = R/4$. $R_{DE} = R_{EC} = R/8$. $R_{EB}$, $R_{DA}$, $R_{AB}$, $R_{BC}$ are in series: $\frac{R}{8} + \frac{R}{4} + \frac{R}{4} + \frac{R}{4} = \frac{7R}{8}$. Parallel with $R_{EC} = R/8$: $R_{\text{eq}} = \frac{\frac{7R}{8} \times \frac{R}{8}}{\frac{7R}{8} + \frac{R}{8}} = \frac{7R}{64}$.
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