Question

Consider the circuit shown in the diagram. Find the current in 3 ohm resistor.

Answer 1

Answer:

The current in 3 ohm resistor is $\dfrac{2}{3}\ A$

Explanation:

Given that,

Resistance $R_{1}=10\Omega$

Resistance $R_{2}=3\Omega$

Resistance $R_{3}=6\Omega$

According to figure,

R₂ and R₃ are connected in parallel

The equivalent resistance is

$\dfrac{1}{R}=\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}$

$\dfrac{1}{R}=\dfrac{1}{3}+\dfrac{1}{6}$

$\dfrac{1}{R}=\dfrac{1}{2}$

$R=2\Omega$

R and R₁ are connected in series

The equivalent resistance is

$R'=R+R_{1}$

$R'=2+10$

$R'=12$

Using ohm's law

The current is defined as,

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

$I=\dfrac{12}{12}$

$I=1\ A$

The current in the circuit is 1 A.

Now, The voltage through AB

$V' =I\times R$

$V'=1\times10$

$V'=10\ volt$

The voltage through BC

$V''=V-V'$

$V''=12-10$

$V''=2\ volt$

Now, The current in 3 ohm resistor is

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

$I=\dfrac{2}{3}\ A$

Hence, The current in 3 ohm resistor is $\dfrac{2}{3}\ A$

Answer 2

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