Question

A p.d of 6V is applied to two resistors of 3Ω and 6Ω connected in parallel . Calculate (i) equivalent resistance (ii) total current (ii) The current flowing in the 3Ω resistor .

Answer 1

Solution :

⏭ Given:

✏ Two resistors of resistance 3Ω and 6Ω are connected in parallel with p.d. 6V

⏭ To Find:

• Equivalent resistance
• Total current flow in circuit
• Current flow in 3Ω resistor

⏭ Formula:

✏ Formula of eq. resistance in parallel connection is given by...

$\bigstar \: \boxed{ \tt{ \large{ \pink{R_{eq} = \dfrac{R_1 \times R_2}{R_1 + R_2}}}}} \: \bigstar$

✏ As per ohm's law, relation between potential difference, resistance and current is given by...

$\bigstar \: \boxed{ \tt{ \large{ \purple{V = I \times R}}}} \: \bigstar$

⏭ Calculation:

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• Equivalent resistance

$\dashrightarrow \sf \: R_{eq} = \dfrac{3 \times 6}{3 + 6} \\ \\ \dashrightarrow \sf \: R_{eq} = \dfrac{18}{9} \\ \\ \dashrightarrow \: \boxed{ \tt{ \red{\large{R_{eq} = 2 \: \Omega}}}} \: \orange{ \bigstar}$

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• Total current flow

$\implies \sf \: V = I_{net} \times R_{eq} \\ \\ \implies \sf \: 6 = I_{net} \times 2 \\ \\ \implies \sf \: I_{net} = \dfrac{6}{2} \\ \\ \implies \: \boxed{ \tt{\large{ \green{I_{net} = 3 \: A}}}} \: \orange{ \bigstar}$

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• Current flow in 3Ω resistor

$\rightarrowtail \sf \: V = I \times R \\ \\ \rightarrowtail \sf \: 6 = I \times 3 \\ \\ \rightarrowtail \sf \: I = \dfrac{6}{3} \\ \\ \rightarrowtail \: \boxed{ \tt{ \large{\blue{I = 2 \: A}}}} \: \orange{ \bigstar}$

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⏭ Additional information:

• Ohm's law is not applicable for semi-conductor devices.
• Potential difference remains same across all resistors in parallel connection.
• Current is fundamental quantity.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Equivalent\:resistance=2\Omega}}}$

$\green{\tt{\therefore{Total\:current\:flow=3\:A}}}$

$\green{\tt{\therefore{Current\:flow\:in\:3\Omega\:resistance=2\:A}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Potential \:difference (v)= 6 \: v \\ \\ \tt: \implies Parallel\: resistance = 3 \Omega \: and \: 6 \Omega \\ \\ \red{\underline \bold{To \: Find :}}\\ \tt: \implies Equivalent \: resistance( R_{equivalent}) = ? \\ \\ \tt: \implies Total \: current(I) = ? \\ \\ \tt: \implies Current \: flow \: in \: 3 \Omega \: resistance = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies R_{equivalent} = \frac{1}{R_{1} } + \frac{1}{R_{2} } \\ \\ \tt: \implies R_{equivalent} = \frac{1}{3} + \frac{1}{6} \\ \\ \tt: \implies R_{equivalent} = \frac{2 + 1}{6} \\ \\ \tt: \implies R_{equivalent} = \frac{3}{6} \\ \\ \green{\tt: \implies R_{equivalent} = 2\Omega} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies V = IR \\ \\ \tt: \implies 6 = I \times 2 \\ \\ \tt: \implies I= \frac{6}{2} \\ \\ \green{\tt: \implies I= 3 \: A} \\ \\ \bold{Current \: flow \: in \: 3 \Omega} \\ \tt: \implies V = I R_{1} \\ \\ \tt: \implies 6 = I\times 3 \\ \\ \tt: \implies I = \frac{6}{3} \\ \\ \green{\tt: \implies I= 2 \: A}$