Question

The potential difference between the points A and B in the circuit shown here is 16V. Which is/are the correct statement(s) out of the following?

• A. The current through the $2\Omega$ resistor is 3.0A.
• B. The current through the $4\Omega$ resistor is 2.5A.
• C. The current through the $3\Omega$ resistor is 1.5A.
• D. Potential difference between the terminals of 9 V battery is 11 V.

Answer 1

Answer: (C)

The current through the $3\Omega$ resistor is 1.5A.

In the figure given

let voltages at A,B,C,D be $V_A,V_B,V_C,V_D$.

Let $V_A>V_B$.

given $V_A-V_B=16V$

let current from A to B be ${}^{\prime }{i}^{\prime }$ (through r1,r4,r5)

let current from C to D through r2 be $i_1$, then current from r3 will be $i-i_1$ from C to D.

On applying 'Kirchhoff's voltage law' in the closed loop with 9V source :-

$9-2(i-i_1)+1i_1=0$

$\Rightarrow i_1=\frac{2i-9}{3}$.....(1)

On applying 'Kirchhoff's voltage law' from A to B:-

$V_A-4i-9-1i_1+3-1i-3i-V_B=0$

$\Rightarrow 16-8i-6-i_1=0$ ($\because V_A-V_B=16$)

$\Rightarrow 30-26i+9=0(\because$ from equation (1))

$\Rightarrow i=1.5A$

$\Rightarrow i_1=-2A$

So current through r1,r4,r5 is 1.5$A$.

current through r2 is 2$A$.

current through r3 is 0.5$A$.