Q. 74.2( 37 Votes )

# 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

Answer :

A. When both S_{1} and S_{2} are closed, R_{4} is short circuited.

R_{3} and (R_{1}||R_{2}) are in series

Effective resistance of the circuit R_{effective} =

⇒

Let the applied voltage be V.

Current in the circuit

⇒

B. When both S_{1} and S_{2} are open, R_{3} , R_{1} and R_{4} are in series.

The effective resistance of the circuit,

R_{effective} = R_{3} + R_{1} + R_{4}

Let the applied voltage be V.

Current in the circuit I = V/R_{effective}

C. When S_{1} is closedbut S_{2} is open, R_{3}, (R_{1}||R_{2}) and R_{4} are in series.

As S_{1} is closed, R_{1} and R_{2} are parallel to each other.

The effective resistance of the circuit is

R_{effective} = R_{3} + (R_{1}||R_{2}) + R_{4} ( When R_{1}||R_{2} )

=

Let the applied voltage be V

Current in the circuit I = V/R_{effective}

I =

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Umesh has two bulbs having resistances of and He wants to connect them in a circuit, but if he connects them one at a time the filament gets burnt. Answer the following.

A. Which method should he use to connect the bulbs?

B. What are the characteristics of this way of connecting the bulbs depending on the answer of A above?

C. What will be the effective resistance in the above circuit?

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