Given Vs = 154 voltsR = 81 ohmsL= 63 mHF = 100 HzCalculate the phase of the phasor current I in RADIANSChoose a value of phase which is between -pi and +pi.
Question
Given:
- Vs = 154 volts
- R = 81 ohms
- L = 63 mH
- F = 100 Hz
Calculate the phase of the phasor current I in RADIANS
- Choose a value of phase which is between -π and +π.
Solution
Step 1: Convert the inductance from millihenries to henries.
1 millihenry = 1e-3 henries So, L = 63 millihenries = 63 * 1e-3 = 0.063 henries
Step 2: Calculate the reactance (Xl) of the inductor using the formula:
Xl = 2 * π * F * L
where: π = 3.14159 (approx) F = frequency = 100 Hz L = inductance = 0.063 henries
Substituting the values, we get:
Xl = 2 * 3.14159 * 100 * 0.063 = 39.79 ohms (approx)
Step 3: Calculate the phase angle (θ) of the phasor current. The phase angle is the arctangent of the ratio of the reactance to the resistance.
θ = arctan(Xl / R)
Substituting the values, we get:
θ = arctan(39.79 / 81) = 0.44 radians (approx)
However, since the current lags the voltage in an inductive circuit, the phase angle should be negative.
So, the phase of the phasor current is -0.44 radians.
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