Question

8. Two bulbs have resistances 2 points
in the ratio 1:2. If they are
joined in series, the energy
consumed in them is in the
ratio -
2:1
O 1:2
0 4:1
O 1:1​

Answer 1

Answer:

b) 1:2

Steps:

Power = $\\\tt I^2R$

Power of Bulb 1 = $\\\tt I^2R_1$

And power of Bulb 2 = $\\\tt I^2R_2$

Ratio of powers of Bulb 1 to Bulb 2 (using  $\\\tt R_1 : R_2 = 1:2$ in the expression):

$\\\tt \dfrac{I^2R_1}{I^2R_2} = \dfrac{1}{2}$

Explanation:

Why did I used $\\\tt I^2R$ and not $\\\tt \dfrac{V^2}{R}$ .

The circuit is in series and so the current through each bulb will be equal but not the voltage. if I had used the second formula instead of first one it would've complicated the calculations.

If the question has bulbs in parallel I'd have preferred 2nd formula since V in a parallel connection is same for the resistors.

Answer 2

Answer:

Given :-

Two bulbs have resistances 2 points

in the ratio 1:2.

To Find :-

Ratio of energy

Solution :-

Let the resistance be R and R'

We know that

Power = (Current)² × Resistance

I²R/I²R' = 1/2

P/P' = 1/2

Hence,

Ratio is 1:2