Question

in the above circuit , if the current reading in the ammeter is 2 A what would be the value of R1​

Answer 1

Value of R₁ = 30 Ω

Given:

• Circuit
• Current through Ammeter is 2A
• Voltage = 30V

To Find:

• Value of R₁

Solution:

• V = IR
• V = Voltage
• I = Current
• R = Resistance
• Resistance in series are added  R = R₁ + R₂ + ... + Rₙ
• Equivalent Resistance in Parallel    1/R = 1/R₁ + 1/R₂ + ... + 1/Rₙ

Step 1:

Use R = V/I and find Equivalent  Resistance of circuit by substituting V = 30 and I = 2

R = 30/2

R = 15 Ω

Step 2:

Find Equivalent resistance of circuit

6 + 6  +  1/(1/5 + 1/10  + 1/R₁)

= 12 + 10R₁/(2R₁ + R₁  + 10)

= 12 + 10R₁/(3R₁  + 10)

( as 5 , 10 and R₁ are in parallel  and their equivalent is in series with 6 and 6)

Step 3:

Equate Equivalent resistance and solve for R₁

15 =  12 + 10R₁/(3R₁ + 10)

=> 3 = 10R₁/(3R₁ + 10)

=> 30 + 9R₁ = 10R₁

=> R₁ = 30

Value of R₁ = 30 Ω