Question

In the circuit diagram shown below, V A
and VB
are the potentials at points A and B respectively. Then,
VA
– VB

is

A) –10 V
B) –20 V
C) 0 V
D) 10 V​

Answer 1

D) 10V

I hope it helps you

Answer 2

Given:

A circuit diagram with 4 resistors attached to a battery of 30V.

Points A and B between resistors 10Ω and 20Ω and between 10Ω and 5Ω.

To Find:

VA - VB

Solution:

Let i be the total current flowing from the battery.

As the current reaches the arrangement of resistors, it gets divided. Let the current in the upper branch be i₁ and in the lower branch be i₂.

Using Kirchhoff’s Current Law (KCL), we know that

i =  i₁ + i₂     - (1)

Since the current divides in the opposite ratio of the resistors, so:

i₁ = $\frac{10+5}{10+5+10+20} X i$

= 15 i / 45

= i / 3

Similarly, i₂ = $\frac{10+20}{10+20+10+5} X i$

= 30 i / 45

= 2i / 3

Applying KVL to the circuit,

30 - 10 i₁ = VA

or VA = 30 - (10 i /3)      -(2)

Again applying KVL in the lower branch,

30 - 10 i₂ = VB

or VB = 30 - (20 i / 3)   -(3)

Subtracting equations (1) and (2),

VA - VB = 30 - (10 i /3) - 30 + (20 i / 3)

or VA - VB = 20 i - 10i / 3

= 10i / 3     - (4)

The net resistance in the circuit = $\frac{30X15}{30+15}$

= 10Ω

Using Ohm's law,

I = V / R = 30 / 10

or I = 3 A    - (5)

Substituting (5) in (4),

VA - VB = 10 X 3 / 3

= 10 V

Hence, VA - VB is 10 V.