Resistances and are connected as shown in the figure. S1 and S2 are two keys. Discuss the current flowing in the circuit in the following cases.

A. Both and are closed.

B. Both and are open.

C. is closed but is open

A. When both S₁ and S₂ are closed, R₄ is short circuited.

R₃ and (R₁||R₂) are in series

Effective resistance of the circuit R_effective =

⇒

Let the applied voltage be V.

Current in the circuit

⇒

B. When both S₁ and S₂ are open, R₃ , R₁ and R₄ are in series.

The effective resistance of the circuit,

R_effective = R₃ + R₁ + R₄

Let the applied voltage be V.

Current in the circuit I = V/R_effective

C. When S₁ is closedbut S₂ is open, R₃, (R₁||R₂) and R₄ are in series.

As S₁ is closed, R₁ and R₂ are parallel to each other.

The effective resistance of the circuit is

R_effective = R₃ + (R₁||R₂) + R₄ ( When R₁||R₂ )

=

Let the applied voltage be V

Current in the circuit I = V/R_effective

I =