Question

A circuit consist of 2-parallel resistors having resistance of 20 and 30 Ω respectively connected in series with 15 Ω resistance. If current through 15 Ω resistance is 3 A, Find (i) current through 20 Ω and 30 Ω resistors and (ii) voltage across whole circuit.​

Answer 1

Explanation:

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Answer 2

Given:-

• $\bf R_{1} = 20Ω$
• $\bf R_{2} = 30Ω$
• they both are connected in parallel and their combination is connected in series with 15Ω Resistor
• Current through 15Ω = 3A

To find:-

• Current through 20Ω and 30Ω
• Voltage across the entire circuit.

Formulas:-

$\implies$$\underline\red{\boxed{\bf \dfrac{1}{R_{eq}} = \dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}...}}$

$\implies$$\underline\pink{\boxed{\bf V = IR}}$

$\implies$$\underline\orange{\boxed{\bf current = \dfrac{Voltage}{Resistance}}}$

Solution:-

$\dashrightarrow$ $\sf \dfrac{1}{R} = \dfrac{1}{20}+\dfrac{1}{30}$

$\dashrightarrow$ $\sf \dfrac{1}{R} = \dfrac{3+2}{60}$

$\dashrightarrow$ $\sf \dfrac{1}{R} = \dfrac{5}{60}$

$\dashrightarrow$ $\sf R = 12$

• Now, we know that 12Ω and 15Ω are in series and 3A of current is flowing through the 15Ω

• In series combination, current remains constant hence, the amount of current through 12Ω is also 3A

We know that:-

$\dashrightarrow$ $\underline\pink{\boxed{\sf V = IR }}$

hence, according to Ohm's law:-

$\dashrightarrow$ $\sf Voltage = 3×12$

$\dashrightarrow$ $\sf Voltage = 36 V$

• We know that, Voltage remains constant in parallel connection. Hence, the voltage across 20Ω and 30Ω will be 36 V.

Current across 20Ω :-

$\dashrightarrow$ $\sf Current = \dfrac{36}{20}$

$\dashrightarrow$ $\sf Current = 1.8A$

Current across 30Ω :-

$\dashrightarrow$ $\sf current = \dfrac{36}{30}$

$\dashrightarrow$ $\sf Current = 1.2A$

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2.] Voltage across the entire circuit:-

• Total voltage will be equal to Voltage across 12Ω + voltage across 15 Ω

Voltage across 15Ω :-

$\dashrightarrow$ $\sf Voltage = 15×3$

$\dashrightarrow$ $\sf Voltage = 45V$

and voltage across 12Ω = 36 V (as calculated above)

so, total voltage = 36+45 = 81 V