Question

what is the current if 12 ohm and 4 ohm resistors are connected in parallel and 12v potential difference is applied ​

Answer 1

Answer:

4 A

Explanation:

As per the provided information in the given question, we have :

• Resistors of 12Ω and 4Ω are connected in parallel.
• Potential difference of 12V is applied.

To calculate : Current (I).

In order to calculate current flowing in the circuit, firstly we need to calculate the equivalent resistance of the circuit.

Whenever the resistors are connected in parallel combination, equivalent resistance is given by :

$\longrightarrow \sf { \dfrac{1}{R_P} = \dfrac{1}{R_1} + \dfrac{1}{R_2}}$

• $\sf R_1$ = 12Ω
• $\sf R_2$ = 4Ω

Substitute the values.

$\longrightarrow \sf { \dfrac{1}{R_P} =\Bigg \lgroup \dfrac{1}{12} + \dfrac{1}{4} \Bigg \rgroup \; \Omega}$

$\longrightarrow \sf { \dfrac{1}{R_P} =\Bigg \lgroup \dfrac{1 + 3}{12} \Bigg \rgroup \; \Omega}$

$\longrightarrow \sf { \dfrac{1}{R_P} = \dfrac{4}{12} \; \Omega}$

On reciprocating both sides,

$\longrightarrow \sf { R_P = \dfrac{12}{4} \; \Omega}$

$\longrightarrow \underline{\boxed{\red{ \sf { R_P = 3 \; \Omega}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

Now, by using Ohm's Law,

$\longrightarrow \sf { V = IR}$

• V denotes potential difference
• I denotes current
• R denotes resistance

$\longrightarrow \sf { 12 = I \times 3}$

$\longrightarrow \sf { \cancel{\dfrac{12}{3}} \; A= I }$

$\longrightarrow \underline{\boxed{\red{ \sf {4 \; A= I}}}}$

Therefore, the current flowing in the circuit is 4 Ampere.

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

What is the current if 12 ohm and 4 ohm resistors are connected in parallel and 12 V potential difference is applied ?

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

• Current flowing through circuit is 4 Ampere .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• Resistors of 12 ohm and 4 ohm are connected in parallel .

• Potential Difference ( V ) = 12

• $\sf R_1 = 12 \: Ω$

• $\sf R_2 = 4 \: Ω$

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• Value of current ( I ) .

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\purple{ \boxed{ \begin{array}{l} \textsf{Resistance of circuit when two resistors} \\ \\ \textsf{are connected in parallel is :-} \\ \\ \displaystyle \sf \frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2} \end{array}}}$

$\purple{ \boxed{ \begin{array}{l} \red{ \bigstar \: \textsf{Ohm's Law : }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \longrightarrow \sf V = IR \end{array}}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

$\red{ \underline{ \underline{\textsf{Total resistance of circuit : }}}}$

$\displaystyle \sf \longrightarrow \frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2} \: \\ \\ \displaystyle \sf \longrightarrow \frac{1}{R_P} = \frac{1}{12} + \frac{1}{4} \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{1}{R_P} = \frac{1 + 3}{12} \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{1}{R_P} = \frac{4}{12} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{1}{R_P} = \frac{1}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow R_P = 3 \: Ω \: \: \: \: \: \: \: \: \: \: \: \:$

$\red{ \underline{ \underline{\textsf{Calculating Current ( I ) : }}}}$

$\longrightarrow \sf V = IR \: \: \: \: \:\\ \\\longrightarrow \sf 12 = I(3) \: \\ \\\longrightarrow \sf 12 = 3I \: \: \: \: \\ \\ \longrightarrow \sf 3I = 12 \: \: \: \: \\ \\ \longrightarrow \sf I = \frac{12}{3} \: \: \: \: \: \\ \\ \longrightarrow \sf I =4 \: A \: \: \: \:$

$\purple{\boxed{\begin{array}{l} \textsf{Current flowing through circuit is 4 Ampere .} \end{array}}}$

$\green{ \large \underline{ \mathbb{\underline{KNOW \: MORE: }}}}$

• Resistance

Resistance is a measure of the opposition to current flow in an electrical circuit .

• Potential Difference

Potential difference is the difference in the amount of energy that charge carriers have between two points in a circuit .

• Current

Current is the rate of flow of electric charge .

• Ohm's Law

Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

• Ampere

One ampere is equal to a flow of one coulomb of charge per second .

• Volt

One Volt is defined as energy consumption of one joule per electric charge of one coulomb .

• Ohm

One ohm is equal to the resistance of a conductor through which a current of one ampere flows when a potential difference of one volt is applied to it .