A p.d of 6V is applied to two resistors of 3Ω and 6Ω connected in pa

1.	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» 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: _________________________________ Equivalent resistance $\dashrightarrow \sf \: R_{eq} = \dfrac{3 \times 6}{3 + 6} \\ \\ \dashrightarrow \sf \: R_{eq} = \dfrac{18}{9} \\ \\ \dashrightarrow \: \boxed{ \tt{ \red{\large{R_{eq} = 2 \: \Omega}}}} \: \orange{ \bigstar}$ _________________________________ Total current flow $\implies \sf \: V = I_{net} \times R_{eq} \\ \\ \implies \sf \: 6 = I_{net} \times 2 \\ \\ \implies \sf \: I_{net} = \dfrac{6}{2} \\ \\ \implies \: \boxed{ \tt{\large{ \green{I_{net} = 3 \: A}}}} \: \orange{ \bigstar}$ _________________________________ Current flow in 3Ω resistor $\rightarrowtail \sf \: V = I \times R \\ \\ \rightarrowtail \sf \: 6 = I \times 3 \\ \\ \rightarrowtail \sf \: I = \dfrac{6}{3} \\ \\ \rightarrowtail \: \boxed{ \tt{ \large{\blue{I = 2 \: A}}}} \: \orange{ \bigstar}$ _________________________________ ⏭ 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.

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»

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:

_________________________________

Equivalent resistance

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

_________________________________

Total current flow

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

_________________________________

Current flow in 3Ω resistor

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

_________________________________

⏭ 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.

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 .

Solution :

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