Question

pls answer this question​

Answer 1

Question :

The three resistors of resistance 5 Ω, 10 Ω and 30 Ω, are connected with a 12 V battery in parallel circuit. Determine :-

⠀⠀⠀⠀a) Total current in the circuit.

⠀⠀⠀⠀b) Equivalent resistance in the circuit.

Answer :

• Total current in the circuit, I = 4 A
• Equivalent resistance in the circuit, Rₑ = 3 Ω

Explanation :

Given :

• Resistance in the resistor, R₁ = 5 Ω
• Resistance in the resistor, R₂ = 10 Ω
• Resistance in the resistor, R₃ = 30 Ω
• Voltage in the circuit, V = 12 V

To find :

• Total current in the circuit, I = ?
• Equivalent resistance in the circuit, Rₑ = ?

Knowledge required :

• Formula for total resistance in a parallel circuit :- 1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ

[Where : Rₑ, R are the equivalent resistance and resistance in the n resistors, respectively]

• Equation for the ohm's law :- V = IR

[Where : V, I and R are the Voltage in the circuit, Current flowing through the circuit and the Resistance in the circuit, respectively]

Solution :

First, let us find the total resistance in the equation :

⠀By using the formula for total resistance in a parallel circuit and substituting the values in it, we get :

⠀⠀=> 1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃

⠀⠀=> 1/Rₑ = 1/5 + 1/10 + 1/30

⠀⠀=> 1/Rₑ = (6 + 3 + 1)/30

⠀⠀=> 1/Rₑ = 10/30

⠀⠀=> Rₑ = 30/10

⠀⠀=> Rₑ = 3

⠀⠀⠀⠀⠀∴ Rₑ = 3 Ω (Ans.)

Hence, the total resistance in the circuit is 3 Ω.

Now, to find the current in the circuit :

⠀By using the equation for ohm's law and substituting the values in it, we get :

⠀⠀=> V = IR

⠀⠀=> 12 = I × 3

⠀⠀=> 12/3 = I

⠀⠀=> 4 = I

⠀⠀⠀⠀⠀∴ I = 4 A (Ans.)

Hence, the total current in the circuit is 4 A.

Answer 2

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Question}}}}}$

✠ The three resistors of resistance 5 Ω, 10 Ω and 30 Ω are connected with 12V battery in parallel. Determine –

⒈ Total current in the circuit.

⒉ Equivalent circuit resistance

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Given \; that}}}}}$

◕ The three resistors of resistance 5 Ω, 10 Ω and 30 Ω are connected with 12V battery in parallel.

$\; \; \; \; \; \; \; \; \; \; \; \; \; \; \;{\sf{Means,}}$

↠ Resistance in the resistor, R₁ = 5Ω

↠ Resistance in the resistor, R₂ = 10Ω

↠ Resistance in the resistor, R₃ = 30Ω

↠ Voltage in circuit = 12V

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{To \; find}}}}}$

↠ Total current in the circuit.

↠ Equivalent circuit resistance

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Solution}}}}}$

↠ Total current in the circuit = 4A

↠ Equivalent circuit resistance = 3Ω

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Using \: concept}}}}}$

↠ Formula to find resistance.

↠ Formula of Ohm's Law

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Using \: formula}}}}}$

↠ 1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃ (parallel)

↠ V = IR

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let us find the total resistance firstly, in the circuit and we get the equivalent circuit resistance.

⇢ 1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃

⇢ 1/Rₑ = 1/5 + 1/10 + 1/30

• Let us take the LCM.

⇢ 1Rₑ = (6+3+1) / 30

⇢ 1Rₑ = 10/30

⇢ 1Rₑ = 1/3

⇢ Rₑ = 3/1

⇢ Rₑ = 3Ω

${\frak{Therefore, \: 3 \: ohm \: is \: equivalent \: circuit \: resistance}}$

~ Now let's find the total current in the circuit by using formula of ohm's law.

⇢ V = IR

⇢ 12 = I(3)

⇢ 12 = I × 3

⇢ 12/3 = I

⇢ 4 = I

⇢ I = 4A

${\frak{Therefore, \: 4 \: A \: is \: total \: current \: in \: circuit}}$

$\: \: \: \: \: \: \:{\large{\bold{\rm{\underline{Knowledge \: related \: to \: this \: Topic}}}}}$

Combination of resistance -

Various resistance can be combined to form a network mainly in two ways,

• Series combination.
• Parallel combination.

Series combination -

In this equivalent resistance is equal to the sum of the resistance of individual conductor. (R = R₁ + R₂ + ...... Rƞ)

Parallel combination -

In this the reciprocal of equivalent resistance is equal to the sum of the reciprocal of individual resistances.

(1/2 = 1/R₁ + 1/R₂ + ..... + 1/Rƞ)

According to the question, it's formula is 1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃.

Where,

★ R is equivalent resistance.

★ Rₑ is n resistor

Ohm's law -

If physical conditions like temperature, intensity of the light etc remains unchanged then electric current flowing through a conductor is directly proportional to the potential difference across it's end. It is given by, V ∞ I or V = RI.

Where,

★ V is potential difference

★ I is current.