Question

A circuit is set up as shown in the figure. Calculate the current and potential difference across R₁ , R₂ and R₃ , when 

a) keys K₁ and K₂ are both closed, 

b) key K₁ is closed and K₂ is open, 

c) key K₁ is open and K₂ is closed.

Answer 1

a) When both the keys K₁ and K₂ are closed : 

The resistors R₁ and R₃ are parallel. 

So resultant resistance R_p =

\(\frac {R_1\,R_3}{R_1+R_3} = \frac {6\times4}{6+4} = 2.4Ω\)

The resistor R₁ and R_p are in series as shown in figure.

Total resistance of circuit R_s = R₁ + R_p = 6 + 2.4 = 8.4 Ω

Current I = V/R_s = 4.2/8.4 = 0.5 = A

Potential difference across R₁ is V₁ = IR₁ = 0.5 × 6 = 3V. 

Potential difference across the combination of R₂ and R₃ is 

V’ = V – V₁ = 4.2 – 3 = 1.2 V. 

Now since R₂ and R₃ are in parallel, 

Potential difference across R₂ = 

Potential difference across R₃ = V’ = 1.2 V

Current through R₂ is I₂ = V'/R₂ = 1.2/6 = 0.2 A

Current through R₃ is I₃ = V'/R₃ = 1.2/4 = 0.3 A

b) When the key K₁ is closed and key K₂ is open : 

The resistor R₃ will not be in circuit. 

The resistors R₁ and R₂ are in series. 

Total, resistance R_s = R₁ + R₂ = 6 + 6=12 Ω.

Current I = V/R_s = 4.2/12 = 0.35 A

The same current will flow through each resistor R₁ and R₂. 

Potential difference across R₁ is V₁ = IR₁ = 0.35 × 6 = 2.1 V. 

Potential difference across R₂ is V₂ = IR₂ = 0.35 × 6 = 2.1 V.

The current and potential difference across R₃ will be zero.

c) When key K₁ is open and key K₂ is closed : 

No current flows through R₁ R₂ and R₃ since the circuit is incomplete. Hence potential difference across R₁, R₂ and R₃ is zero.