Question

Sides of a quadrilateral circumscribed by a circle have resistance per unit length of $1\Omega /m.$ Side AB is $4m$, side AD is $3m$ and AC is $5m$. AC is diameter of circle. The resistance of circle is zero but its diameter has a resistance per unit length of $1\Omega /m.$ Equivalent resistance between point B and D is (Write upto two digits after the decimal point.)

Answer 1

Angle in a semi-circle is ${90}^o$.

For loop ABC,
$3i_2+5(i_2-i_1)=4i_1$
$\Rightarrow 8i_2=9i_1$ ...(1)
$ϵ=4i_1+3i_2$ ...(2)
and $ϵ=(i_1+i_2)R_{eq}$ ...(3)


Using (1), (2) and (3), $R_{eq}=\frac{59}{17}=3.47\Omega$