Question

If the current through the branch BD of the circuit, shown, is zero. Find the resistance R and current I though
it.

Answer 1

Given that,

Resistance is

$R_{1}=1.5\ \Omega$

$R_{2}=1\ \Omega$

$R_{3}=R$

$R_{4}=4\ \Omega$

$R_{5}=2\ \Omega$

If the current through the branch BD of the circuit is zero.

We need to calculate the value of R

Using wheatstone bridge

$\dfrac{P}{Q}=\dfrac{R}{S}$

Put the value into the formula

$\dfrac{1.5}{1}=\dfrac{R}{4}$

$R=\dfrac{4\times1.5}{1}$

$R=6\ \Omega$

We need to calculate the current through R

Using ohm's law

$V = IR$

$I=\dfrac{V}{R}$

Put the value into the formula

$I=\dfrac{10}{6}$

$I=1.6\ A$

Hence, The resistance is 6 Ω and 1.6 A.