Question

Find the value of $R$ so that no deflection is noticed in the galvanometer when the switch $S$ is closed or open

• A. $4\Omega$
• B. $8\Omega$
• C. $6\Omega$
• D. None of these

Answer 1

The correct option is B $8\Omega$

Given circuit is equivalent to the Wheatstone bridge. When switch is open the current will not flow through the galvanometer(no deflection) since circuit remains incomplete.

When switch is closed, galvanometer shows no deflection if bridge is balanced i.e.

$\frac{R_{AC}}{R_{CB}}=\frac{R_{AD}}{R_{DB}}$
$\frac{3}{1+1}=\frac{3+3}{\left(\frac{8R}{R+8}\right)}$

$\frac{3}{2}=\frac{6}{\left(\frac{8R}{R+8}\right)}$

$\frac{1}{\left(\frac{8R}{R+8}\right)}=\left(\frac{3}{2}\right)\left(\frac{1}{6}\right)$

$\frac{1}{\left(\frac{8R}{R+8}\right)}=\frac{1}{4}$

$\frac{8R}{R+8}=4$

$8R=4R+32$

$R=8\Omega$