Question

Two bulbs having power of 50W and 25W respectively are connected with the same source. Which has higher resistance?. What is their ratio?​

Answer 1

Answer:

25 W

Explanation:

P = V^2 ÷ R => R = V^2 ÷ P

R1 = V^2 ÷ 50

R2 = V^2 ÷ 25

R1 ÷R2 = 25/50 = 1/2

Therefore, 25 W bulb has a higher resistance, that is, twice the resistance of 50W

Answer 2

Given,

Power of first bulb = P1 = 50W

Power of second bulb  P2 = 25W

To find,

Which bulb has higher resistance?

Solution,

• Both bulbs are connected to the same source therefore both bulbs have the same Voltage(V).

• The formula of power is P = V²/R, where P is power V is voltage, and R is resistance.

• Power is directly proportional to the square of Voltage whereas inversely proportional to Resistance.

       ⇒ P α 1/R

       ⇒ P = k/R.

       ⇒ PR = k,       where k is constant.

• P1R1 = P2R2 where,

P1 = Power of the first bulb.

P2 = Power of the second bulb

R1 = Power of the third bulb

R2 = Power of the fourth bulb.

P1 = 50W and P2 = 25W

⇒   (50)R1= (25)R2

⇒   R1 / R2 = 25 / 50

⇒  R1 / R2 = 1 / 2

⇒   2R1 = R2

Therefore, R2 is twice R1.

Hence, the second bulb with 25W power has higher resistance than the first bulb and the ratio of the resistance of the first bulb to the second bulb is 1/2.