If two electric bulbs have 40w and 60w rating at 220 V, then the ratio of their resistances will be

Answer (Detailed Solution Below)

Option 3 : 2 : 3

Concept:

Electric Power:

  • The rate of consumption of electrical energy is called Electric power.
  • It is given as 

If the Potential difference is constant, Power is inversely proportional to resistance.

 or 

Power × Resistance is constant

Calculation:

Now, Power of resistance 1 (R1) = P1 = 60 W

Now, Power of resistance 2 (R2) = P2 = 40 W

Now, P1 R1 = P2. R2

So, the required ratio is 2 : 3

Additional Information

The power in terms of current and resistance is given as 

P = I 2 R

I is current

So, If the current would have been constant, the power would have been directly proportional to resistance.

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Two electric bulbs A and B are marked 220 V, 40 W and 220 V, 60 W respectively. Which one of these bulbs has higher resistance?

Given, two electrical bulbs.
Potential across first bulb, V1= 220 V
Power of first bulb, P1= 40 W
Potential across second bulb, V2 = 220 V
Power of second bulb, P2 = 60 WNow,

P = V

2/R or R = V2

/P i.e., R ∝ 1/P.Resistance is inversely proportional to power.

Therefore, the first bulb having lesser power has higher resistance.

If two electric bulbs have 40w and 60w rating at 220 V, then the ratio of their resistances will be

If two electric bulbs have 40w and 60w rating at 220 V, then the ratio of their resistances will be
If two electric bulbs have 40w and 60w rating at 220 V, then the ratio of their resistances will be

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If two electric bulbs have 40w and 60w rating at 220 V, then the ratio of their resistances will be

If two electric bulbs have 40 W and 60 W ratings at 220 V, then the ratio of their resistances will be

Options

(a) (3:2) (b) (2:3) (c) (3:4)

(d) (4:3)

Correct Answer:

(3:2)

Explanation:

P = V² / R

⇒ R₁ / R₂ = P₂ / P₁ = 60 / 40 = 3 / 2 = 3 : 2