Question

$\Large\mathtt\green{ }\huge\underline\mathtt\red{question : }$
A circuit consist of two parallel circuit. having a resistance 20ohm and 30ohm respectively connected in series with 15ohm.the current through 15 ohm resistor is 3amps,then find the current through 20ohm and 30ohm resiator respectively.

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Answer 1

EXPLANATION.

A circuit consists of two parallel circuit having resistance 20Ω and 30Ω.

And are connected in series with 15Ω.

Current through 15Ω resistor is 3 ampere.

As we know that,

For parallel combination.

⇒ 1/R_{eq} = 1/R₁ + 1/R₂ + 1/R₃ + . . . . .

Using this formula in the equation, we get.

⇒ 1/R' = 1/20 + 1/30.

⇒ 1/R' = 3 + 2/60.

⇒ 1/R' = 5/60.

⇒ 1/R' = 1/12.

⇒ R' = 12Ω.

It is connected in series with 15Ω.

For series combination.

⇒ R_{eq} = R₁ + R₂ + R₃ + . . . . .

Using this formula in the equation, we get.

⇒ R = 12 + 15 = 27Ω.

As we know that,

OHM'S LAW.

⇒ V = IR.

⇒ V = 3 x 27.

⇒ V = 81 volts.

Current flow through 20Ω.

⇒ V = IR.

⇒ 81 = I x 20.

⇒ I = 81/20.

⇒ I = 4.05 ampere.

Current flow through 30Ω.

⇒ V = IR.

⇒ 81 = I x 30.

⇒ I = 81/30.

⇒ I = 2.7 ampere.

Answer 2

Answer:

Given :-

• A circuit consist of two parallel circuit having a resistance of 20 ohm and 30 ohm respectively connected in series with 15 ohm, the current through 15 ohm resistor is 3 A.

To Find :-

• What is the current through 20 ohm and 30 ohm resistor respectively.

Formula Used :-

$\clubsuit$ Equivalent Resistance for parallel connection :

$\mapsto \sf\boxed{\bold{\pink{\dfrac{1}{R_{eq}} =\: \dfrac{1}{R_1} + \dfrac{1}{R_2} + . . . . + \dfrac{1}{R_n}}}}$

$\clubsuit$ Equivalent Resistance for series connection :

$\mapsto \sf \boxed{\bold{\pink{R_{eq} =\: R_1 + R_2 + . . . . + R_n}}}$

$\clubsuit$ Voltage Formula :

$\mapsto \sf\boxed{\bold{\pink{Voltage =\: Current \times Resistance}}}$

$\clubsuit$ Current Formula :

$\mapsto \sf\boxed{\bold{\pink{Current =\: \dfrac{Voltage}{Resistance}}}}$

Solution :-

For, equívalent resístance for parallel connection :

Given :

• R₁ = 20 Ω
• R₂ = 30 Ω

According to the question by using the formula we get,

$\implies \sf \dfrac{1}{R_{eq}} =\: \dfrac{1}{20} + \dfrac{1}{30}$

$\implies \sf \dfrac{1}{R_{eq}} =\: \dfrac{3 + 2}{60}$

$\implies \sf \dfrac{1}{R_{eq}} =\: \dfrac{5}{60}$

By doing cross multiplication we get,

$\implies \sf 5 \times R_{eq} =\: 60$

$\implies \sf R_{eq} =\: \dfrac{60}{5}$

$\implies \sf\bold{\purple{R_{eq} =\: 12\: Ω}}$

Again, for equívalent resístance for parallel series :

Given :

• R₁ = 12 Ω
• R₂ = 15 Ω

According to the question by using the formula we get,

$\implies \sf R_{eq} =\: 12 + 15$

$\implies \sf\bold{\purple{R_{eq} =\: 27\: Ω}}$

Now, we have to find the voltage :

Given :

• Current = 3 A
• Resistance = 27 Ω

According to the question by using the formula we get,

$\implies \sf Voltage = 3 \times 27$

$\implies \sf \bold{\green{Voltage =\: 81\: V}}$

Now, we have to find the current through 20 ohm and 30 ohm resistor respectively :

${\small{\bold{\underline{\leadsto\: In\: case\: of\: 20\: ohm\: :-}}}}$

Given :

• Voltage = 81 V
• Resistance = 20 Ω

According to the question by using the formula we get,

$\longrightarrow \sf Current =\: \dfrac{81}{20}$

$\longrightarrow \sf\bold{\red{Current =\: 4.05\: A}}$

${\small{\bold{\underline{\leadsto\: In\: case\: of\: 30\: ohm\: :-}}}}$

Given :

• Voltage = 81 V
• Resistance = 30 Ω

According to the question by using the formula we get,

$\longrightarrow \sf Current =\: \dfrac{81}{30}$

$\longrightarrow \sf\bold{\red{Current =\: 2.7\: A}}$

$\therefore$ The current through 20 ohm and 30 ohm resistor respectively is 4.05 A and 2.7 A respectively.