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?

Here we are assuming current to be constant and voltage to be varying.

A. The burning of filament is due to excessive heating when current passes through it. More the resistance of the wire, more is the heating. Therefore, the resistance of the circuit should be decreased which can be done if both the bulbs are connected in parallel.

We know that equivalent resistance in case of parallel combination of two resistances R₁ and R₂ is

In the above case,Ω which is less than the individual resistances of both the wires.

Therefore, both the bulbs should be connected in parallel.

B. Characteristics of a parallel circuit:

1) A parallel circuit has two or more paths for current to flow through and the total current is equal to sum of currents flowing through these paths.

2) Voltage is same across each component of parallel circuit.

3) The current in all the branches is same. As shown in the figure:

C. The effective resistance in the above circuit is given as:

Where R₁ and R₂ are the resistances connected in parallel.

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