Question

A bulb rated 36W and 12V is connected across a 20V cell. What resistance is required to glow it with full intensity.
(a) 1.2
(b) 2.7
(c) 5.8
(d) 7​

Answer 1

Answer:

7 resistance is required

Answer 2

Answer :-

A resistance of 2.7 Ω is required to glow it with full intensity . [Option.b]

Explanation :-

We have :-

→ Voltage of the bulb (V') = 12 V

→ Power of the bulb (P) = 36 W

→ Potential of the cell (V) = 20 V

________________________________

Voltage of the given bulb is 12 V and the source available is of voltage 20 V. Thus, a resistor R₂ is to be connected in series to reduce the current for making it safe for the lamp.

Resistance of the given bulb is :-

⇒ R₁ = (V')²/P

⇒ R₁ = (12)²/36

⇒ R₁ = 4 Ω

Current through the bulb is :-

⇒ I = P/V'

⇒ I = 36/12

⇒ I = 3 A

________________________________

As we have a series connection, so the current through the circuit will be 3 A only. Also the equivalent resistance becomes R = (R₁ + R₂) = (4 + R₂) Ω .

Finally by putting values in Ohm's Law, we get the required resistance as :-

V = IR

⇒ V = I(R₁ + R₂)

⇒ 20 = 3(4 + R₂)

⇒ 4 + R₂ = 6.7

⇒ R₂ = 6.7 - 4

⇒ R₂ = 2.7 Ω

Given :

Voltage of Bulb, V' = 12V

Power of Bulb, P = 36W

Potential of the Cell, V = 20V

To Find :

Resistance Required to Glow the Bulb with Full Intensity.

Solution :

➻ Resistance of the Given Bulb :

⇒ R₁  = (V')²/P

⇒ R₁  = (12)²/36

⇒ R₁  = 144/36

⇒ R₁  = 4Ω

➻ Current passes through the Bulb :

⇒ I = P/V'

⇒ I = 36/12

⇒ I = 3A

_________________________________

It is a Series Connection. So that, The Current passes through the Whole Circuit is 3A . Equivalent Resistance R = (R₁ + R₂)

Now, Substituting the Values in Ohm's Law :

⇒ V = IR

⇒ V = I(R₁  + R₂)

⇒ 20 = 3(4 + R₂)

⇒ 3R₂ = 20 - 12

⇒ R₂ = 8/3

⇒ R₂ = 2.67Ω

FINAL ANSWER :

The Resistance of 2.7Ω is Required to Glow it with Full Intensity.

Thus, Option(B) is the Correct answer.

________________________________________

Extra Information :

Ohm's Law :

It States that “ the current through a conductor between two points is directly proportional to the voltage across the two points and Temperature remains constant ”.

Mathematical Expression for Ohm's Law :

V ∝ I

⇒ V = IR [R is Resistance]