Two bulbs are rated 60w 220v and 40w 220v theratio of their resistances will be

Two bulbs are rated 60 W, 220 V and 60 W, 110 V respectively. Calculate the ratio of their
resistances

Given,Voltage, `V_1` = 220 v

              `V_2` = 110 v

Power, `P_1 = P_2 = p = 60 w`

As  R= `V^2/P`

   `R_1` = `(V_1^2)/P = ((220 xx220))/60`

    `R_2` = `(V_2^2)/P = ((110xx110))/6`

On dividing `R_1` and `R_2`

`R_1/R_2 =(((220xx220))/60)/(((110xx110))/60) =4/1` 

∴ `R_1 : R_2 =4:1`

Concept: Electrical Power

  Is there an error in this question or solution?

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 bulbs have ratings 100 W , 220 V and 60 W , 220 V respectively. Which one has a greater resistance?

Solution

Given

For Bulb A:

power = 100W

voltage = 220V

We know that,

P = V² / R

R = V² / P

= ( 220)² / 100

= 484 ohms..

For Bulb B:

power = 60W

Voltage = 220V

R = V² / P

= (220 )² / 60

= 2420 / 6

= 806.66 ohm...

Therefore, the bulb B has greater resistance.