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The admittance of the electric circuit is represented by Y = (3 + j4). What is the value of resistance in this circuit?
- a)4 / 25 Ω
- b)3 / 25 Ω
- c)4 Ω
- d)3 Ω
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The admittance of the electric circuit is represented by Y = (3 + j4)....
Formula:
The admittance(Y) can be written as:
Y = G ± jB
G = Conductance
B = Susceptance
The impedance(Z) of a circuit can be written as:
Z = R ± jX
R = Resistance
X = Reactance
The relation between impedance and admittance
Z=1Y
Calculation:
Y = 3 + j4
Resistance (R) = 3 / 25 Ω
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The admittance of the electric circuit is represented by Y = (3 + j4)....
To find the resistance in the circuit, we need to calculate the magnitude of the admittance. The magnitude of a complex number is given by the square root of the sum of the squares of its real and imaginary parts.
In this case, the magnitude of the admittance Y = (3 + j4) is:
|Y| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5
The resistance (R) in the circuit is the reciprocal of the magnitude of the admittance:
R = 1/|Y| = 1/5 = 4/25
Therefore, the value of resistance in this circuit is 4/25.
In this case, the magnitude of the admittance Y = (3 + j4) is:
|Y| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5
The resistance (R) in the circuit is the reciprocal of the magnitude of the admittance:
R = 1/|Y| = 1/5 = 4/25
Therefore, the value of resistance in this circuit is 4/25.
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