In the following star circuit diagram (figure), the equivalent resistance between the points A and H will be ..............r

Q: In the following star circuit diagram (figure), the equivalent resistance between the points $A$ and $H$ will be ..............$r$

b (b) Resistance of $CD$ $arm$ = $2r \cos 72^o = 0.62r$ Resistance of $CBFC$ branch $\frac{1}{R} = \frac{1}{{2r}} + \frac{1}{{0.62r}} = \frac{1}{r}\left( {\frac{{2.62}}{{2 \times 0.62}}} \right)$ $\frac{1}{R} = \frac{{2.62}}{{1.24r}}$ $R = \frac{{1.24r}}{{2.62}}$ Equivalent $R' = 2R + r = 2 \times \frac{{1.24r}}{{2.62}} + r$ $ = r\,\left( {\frac{{2.48}}{{2.62}} + 1} \right) = 1.946r$ Because the star circuit is symmetrical about the line $AH$ Equivalent resistance between $A$ and $H$ $\frac{1}{{{R_{eq}}}} = \frac{1}{{R'}} + \frac{1}{{R'}}$ $==>$ ${R_{eq}} = \frac{{R'}}{2} = \frac{{1.946}}{2}r = 0.973r$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

In the following star circuit diagram (figure), the equivalent resistance between the points $A$ and $H$ will be ..............$r$

A$1.944$
B$0.973$
C$0.486$
D$0.243$

Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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