Three voltmeters A, B and C having resistances 1 Ω, 1.5 Ω, and 3 Ω respectively are used in a circuit as shown. When a P.D is applied between X and Y. the reading of the voltmeters are V₁, V₂, and V₃ respectively. Then ______

CONCEPT :

• Ohm's Law: A law that states that electric current is proportional to voltage and inversely proportional to resistance. Mathematically,

V = IR

where R is the resistance, I is current, and V is the voltage across the conductor.

• In the Series circuit, the equivalent resistance is the algebraic sum of all the resistances.

Req = R1 + R2 + R3 +......  (In Series)

• And in the Parallel circuit, the reciprocal of the equivalent resistance is the algebraic sum of all the reciprocal of the resistances.

1/Req = 1/R1 + 1/R2 + 1/R3 +...... (in Parallel circuit)

• Voltage in a Parallel circuit is the same for all the branches.

CALCULATION:

We know that Voltage in a Parallel circuit is the same for all the branches.

Branch B and Branch C are parallel. So the voltage across B and C will be the same.

So V_B = V_C

On combining a parallel combination of 1.5 Ω & 3 Ω ,  the equivalent resistance

\(\frac{1}{R}=\frac{1}{1.5}+\frac{1}{3}\)

R = 1 Ω 

and the resistance of A = 1 Ω