Question

A concave lens of focal length 15 cm for an image 10 cm
from the lens. How far is the object placed from the lens ?
Draw the ray diagram.
4
(h) Prove that the power of an electric bulb is inversely​

Answer 1

QUESTION :-

• A concave lens of focal length 15 cm for an image 10 cm from the lens. How far is the object placed from the lens ? Draw the ray diagram.

ANSWER :-

☆ Given :

• Focal length (f ) = -15 cm
• Distance of image (v) = -10 cm

☆ To prove :

• Object (u)

☆ Formula :

• 1/v–1/u=1/f

☆ Solution :

➦ 1/u = -(1/10) – (1/- 15)

➦ 1/u =1/15 – 1/10

➦ 1/u = -0.033

➦ u = -30 cm ✧

• so the object is placed 30 cm away from the concave lens.

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QUESTION :-

• Prove that the power of an electric bulb is inversely proportional to the resistance

ANSWER :-

☆ Relation Between Power And Resistance :

➙ Power in electronics is the rate of doing work. Resistance is the opposition offered against the flow of electrons. The relation between power and resistance is proportional. In physics, power and resistance can be related using two formulas.

☆ Power and Resistance :

➙ The relation between Power and Resistance can be mathematically expressed in two ways, as follows-

• P = I^2R ✧

Where,

• P is the Power measured in watt
• R is the resistance measured in ohms
• I is the electric current measured in coulombs

• P=V^2/R ✧

Where,

• P is the Power measured in watt
• R is the resistance measured in ohms
• V is the electric potential measured in volts

☆ Power and Resistance Relation :

➙ Both the formula mentioned above gives the relation between power and resistance.

➙ Consider P = I^2R the electric power is directly proportional to resistance keeping I constant. Which implies-

• When power increases, the resistance will also increase keeping current I constant.
• When Resistance decreases, Power also reduces keeping current I constant.

Consider P=V^2/R here, Power P is inversely proportional to Resistance R. which implies that-

For any constant Potential difference

When power is high, resistance will be low.

When power is low, the resistance will be high.

☆ Power and Resistance Formula :

Deriving Power and Resistance formula will concrete the understanding of the concept. Electric power(P) is the measure of the electric current I with Q coulombs of charge passing through a potential difference of V volts in time t seconds.

Mathematically given by-

➦ P=VQ/t=IV ——-(1)

From Ohm’s law, we know that V=IR

Rearranging it for I we get,

➦ I=V/R

Thus, substituting it in equation (1) we get-

➦ P=V^2/R