Question 176: Current Electricity

Question

Four resistances of 15$$\Omega $$, 12$$\Omega $$, 4$$\Omega $$ and 10$$\Omega $$
respectively in cyclic order to form
Wheatstone's network. The resistance that
is to be connected in parallel with the
resistance of 10$$\Omega $$ to balance the network is
_____$$\Omega $$.

Accepted Answer

Wheatstone bridge balance condition
$${{{R_1}} \over {{R_2}}} = {{{R_3}} \over {{R_4}}}$$
$$ \Rightarrow $$ $${{15} \over 4} = {{15} \over {{{10R} \over {10 + R}}}}$$
$$ \Rightarrow $$ 2R = 10 + R
$$ \Rightarrow $$ R = 10 $$\Omega $$

Current Electricity

Four resistances of 15$\Omega , 12\Omega , 4\Omega and 10\Omega respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10\Omega to balance the network is _____\Omega $.

Integer / Numeric Answer Type