Question

Q4 Two 400 resistors and a 200 resistor are connected in parallel with a 12V supply. Calculate their
effective resistance and the current through each resistor. What is the current flowing through the
supply?
​

Answer 1

Answer :

• Effective resistance in the circuit, R = 133.34 Ω
• Current through each resistor; Current through R₁ resistor, I₁ = 0.03 A and Current through R₂ resistor, I₂ = 0.06 A
• Current flowing through the supply, I = 0.09 A

Given :

• Two resistors of resistances R₁ = 400 Ω and R₂ = 200 Ω are connected in parallel
• Voltage through the supply, V = 12 V

To find :

• Effective resistance in the circuit, R =?
• Current through each resistor; Current through R₁ resistor, I₁ =?  and Current through R₂ resistor, I₂ =?
• Current flowing through the supply, I =?

Knowledge required :

• Law of the combination of resistors in parallel

fThis Law states that the reciprocal of equivalent resistance of 'n' number of resistors connected in parallel is equal to the sum of the reciprocals of individual resistances.

      1/R(eq) = 1/R₁ + 1/R₂ + 1/R₃ + ..... 1/Rₙ

• Ohm's Law

       R = V / I

[ Where R is resistance, V is voltage and I is current ]

Solution :

▶Calculating Effective resistance in the circuit (R)

Using law of combination of resistors in parallel combination

→ 1/R = 1/R₁ + 1/R₂

→ 1/R = 1/(400) + 1/(200)

→ 1/R = (1 + 2)/400

→ 1/R = 3/400

→ R = 400/3 = 133.34 Ω

• therefore, Effective resistance in the circuit is equal to 133.34 ohms.

▶Calculating current through each resistor (I₁ and I₂)

Since, Resistor R₁ and R₂ are connected in parallel therefore, there will be same potential difference through both resistors that will be equal to the voltage through the supply, and different current will flow through them.

so,

Using Ohm's law for Resistor R₁

→ R₁ = V / I₁

→ 400 = 12 / I₁

→ I₁ = 12 / 400

→ I₁ = 0.03 A

Now, Using Ohm's law for Resistor R₂

→ R₂ = V / I₂

→ 200 = 12 / I₂

→ I₂ = 12 / 200

→ I₂ = 0.06 A

• Therefore, Current through R₁ and R₂ resistors is 0.03 A and 0.06 A respectively.

▶Calculating Current flowing through the supply (I)

→ Total Current through the circuit, I = I₁ + I₂

→ I = 0.03 + 0.06

→ I = 0.09 A

• Therefore, Total current through the supply is 0.09 A.

Answer 2

Answer :

Effective resistance in the circuit, R = 133.34 Ω

Current through each resistor; Current through R₁ resistor, I₁ = 0.03 A and Current through R₂ resistor, I₂ = 0.06 A

Current flowing through the supply, I = 0.09 A

Given :

Two resistors of resistances R₁ = 400 Ω and R₂ = 200 Ω are connected in parallel

Voltage through the supply, V = 12 V

To find :

Effective resistance in the circuit, R =?

Current through each resistor; Current through R₁ resistor, I₁ =?  and Current through R₂ resistor, I₂ =?

Current flowing through the supply, I =?

Knowledge required :

Law of the combination of resistors in parallel

fThis Law states that the reciprocal of equivalent resistance of 'n' number of resistors connected in parallel is equal to the sum of the reciprocals of individual resistances.

      1/R(eq) = 1/R₁ + 1/R₂ + 1/R₃ + ..... 1/Rₙ

Ohm's Law

       R = V / I

[ Where R is resistance, V is voltage and I is current ]

Solution :

▶Calculating Effective resistance in the circuit (R)

Using law of combination of resistors in parallel combination

→ 1/R = 1/R₁ + 1/R₂

→ 1/R = 1/(400) + 1/(200)

→ 1/R = (1 + 2)/400

→ 1/R = 3/400

→ R = 400/3 = 133.34 Ω

therefore, Effective resistance in the circuit is equal to 133.34 ohms.

▶Calculating current through each resistor (I₁ and I₂)

Since, Resistor R₁ and R₂ are connected in parallel therefore, there will be same potential difference through both resistors that will be equal to the voltage through the supply, and different current will flow through them.

so,

Using Ohm's law for Resistor R₁

→ R₁ = V / I₁

→ 400 = 12 / I₁

→ I₁ = 12 / 400

→ I₁ = 0.03 A

Now, Using Ohm's law for Resistor R₂

→ R₂ = V / I₂

→ 200 = 12 / I₂

→ I₂ = 12 / 200

→ I₂ = 0.06 A

Therefore, Current through R₁ and R₂ resistors is 0.03 A and 0.06 A respectively.

▶Calculating Current flowing through the supply (I)

→ Total Current through the circuit, I = I₁ + I₂

→ I = 0.03 + 0.06

→ I = 0.09 A

Therefore, Total current through the supply is 0.09 A.