Two resistors are connected in parallel across a 24 V supply and a current of 3A flows in
the circuit. If one of the resistors has a resistance of 2 ῼ, determine the value of the other
resistor.
Answers
Correct Question :
Two resistors are connected in parallel across a 24 V supply and a current of 3A flows in the circuit. If one of the resistors has a resistance of 12Ω determine the value of the other resistor.
Given :
Two resistors are connected across a battery of 24V.
Current flow = 3A
One of the two resistors has a resistance of 2Ω.
To Find :
Resistance of other resistor.
Solution :
★ As per ohm's law, current flow in circuit is directly proportional to the applied potential difference at constant temperature [V = I × R]
➠ V = I × R
➠ 24 = 3 × R
➠ R = 24/3
➠ R = 8Ω
Hence equivalent resistance of the parallel connection is 8Ω.
Equivalent resistance of parallel :
- 1/R = 1/R₁ + 1/R₂
By substituting the values,
⭆ 1/8 = 1/12 + 1/R₂
⭆ 1/R₂ = 1/8 - 1/12
⭆ 1/R₂ = (3 - 2) / 24
⭆ 1/R₂ = 1/24
⭆ R₂ = 24Ω
Correct Question :
Two resistors are connected in parallel across a 24 V supply and a current of 3A flows in the circuit. If one of the resistors has a resistance of 12Ω determine the value of the other resistor.
Given :
Two resistors are connected across a battery of 24V.
Current flow = 3A
One of the two resistors has a resistance of 2Ω.
To Find :
Resistance of other resistor.
Solution :
★ As per ohm's law, current flow in circuit is directly proportional to the applied potential difference at constant temperature.. [V = I × R]
➠ V = I × R
➠ 24 = 3 × R
➠ R = 24/3
➠ R = 8Ω
Hence equivalent resistance of the parallel connection is 8Ω.
Equivalent resistance of parallel :
1/R = 1/R₁ + 1/R₂
By substituting the values,
⭆ 1/8 = 1/12 + 1/R₂
⭆ 1/R₂ = 1/8 - 1/12
⭆ 1/R₂ = (3 - 2) / 24
⭆ 1/R₂ = 1/24
⭆ R₂ = 24Ω