Science, asked by arjun642, 7 months ago

class 10 question -36. (a) Two lamps, one is rated 100 W at 220 V, and the other 60 W at 220

V, are connected in parallel to a 220 V supply. Find the current drawn

from the supply line.

(b) Derive an expression when three resistors R1 , R2 and R3 are

connected in parallel in an electric circuit.​

Answers

Answered by ExᴏᴛɪᴄExᴘʟᴏʀᴇƦ
3

\huge\sf\pink{Answer}

☞ Current in the circuit

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\huge\sf\blue{Given}

✭ Qn 1- Two lamps are rated 100 W & 60 W with a pd of 220 V

✭ Qn 2 - There are three resistors connected in parallel

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\huge\sf\gray{To \:Find}

◈ Qn 1 - Current in the circuit?

◈ Qn 2 - Derivation of the formula to find net resistance?

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\huge\sf\purple{Steps}

Question 1

We shall find the current through the circuit with the help of,

\underline{\boxed{\sf P = VI}}

  • P = 100+60 = 160 W
  • V = 220
  • I = ?

Substituting the given values,

\sf P = VI

\sf \dfrac{P}{V} = I

\sf \dfrac{160}{220} = I

\sf \red{I = 0.72 \ A}

Question 2

Given that there are 3 Resistors - R¹,R² & R³ then,

◕ V = constant

\sf I = I_1 + I_2 + I_3 \:\:\: -eq(1)

As per Ohm's law,

\underline{\boxed{\sf V = IR}}

It can also be written as,

\sf \dfrac{V}{R} = I

\sf I_1 = \dfrac{V}{R_1}

\sf I_2 = \dfrac{V}{R_2}

\sf I_3 = \dfrac{V}{R_3}

Substituting the values in eq(1)

\sf I = \dfrac{V}{R_1} + \dfrac{V}{R_2} + \dfrac{V}{R_3}

\sf I = V\bigg\lgroup\dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}\bigg\rgroup

\sf \dfrac{I}{V} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}

\sf \orange{\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}}

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