Question

a circuit consist of two parallel resistor having resistance of 20 ohm and 30 ohm respectively connected with series of 15 ohm.if current through 15 ohm is 3A what is the total power​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Two resistors of 20Ω & 30Ω are connected in parallel

✭ This combination is then connected in Series with a 15Ω resistor

✭ Current through the 15Ω resistor is 3A

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Total power in the circuit?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we may first find the net resistance in a circuit, then with that we may find the total power with the help of,

$\displaystyle\underline{\boxed{\sf P = I^2R }}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

Equivalent Resistance of the parallel combination is given by,

$\displaystyle\underline{\boxed{\sf \dfrac{1}{R_{eq}} = \dfrac{1}{R_1}+\dfrac{1}{R_2}...+\dfrac{1}{R_n}}}$

• $\displaystyle\sf R_1 = 20 \ \Omega$
• $\displaystyle\sf R_2 = 30 \ \Omega$

Substituting the given values,

➝ $\displaystyle\sf \dfrac{1}{R_{eq}} = \dfrac{1}{R_1}+\dfrac{1}{R_2}...+\dfrac{1}{R_n}$

➝ $\displaystyle\sf \dfrac{1}{R_{eq}} = \dfrac{1}{20}+\dfrac{1}{30}$

➝ $\displaystyle\sf \dfrac{1}{R_{eq}} = \dfrac{50}{20\times 30}$

➝ $\displaystyle\sf \dfrac{1}{R_{eq}} = \dfrac{50}{600}$

➝ $\displaystyle\sf R_{eq} = \dfrac{600}{50}$

➝ $\displaystyle\sf \purple{R_{eq} = 12 \ \Omega}$

So now we shall find the equivalent resistance of the series combination,it is given by,

$\displaystyle\underline{\boxed{\sf R_{eq} = R_1+R_2...+R_n}}$

• $\displaystyle\sf R_1 = 12 \ \Omega$
• $\displaystyle\sf R_2 = 15 \ \Omega$

Substituting the values,

»» $\displaystyle\sf R_{eq} = R_1+R_2...+R_n$

»» $\displaystyle\sf R_{eq} = 12+15$

»» $\displaystyle\sf \orange{R_{eq} = 27 \ \Omega}$

• In a series connection the current through the resistors will be the same, so here it is given that the current across the 15Ω resistor is 3A

Using the formula to find power,

➳ $\displaystyle\sf P = I^2R$

➳ $\displaystyle\sf P = 3^2\times 27$

➳ $\displaystyle\sf P = 9\times 27$

➳ $\displaystyle\sf \pink{P = 243 \ W}$

$\displaystyle\therefore\:\underline{\sf Total \ Power \ will \ be \ 243Watt}$

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