Suppose we have a load in which the voltage is v (t )space equals space 15 space cos (200 pi t plus 65 degree ). Furthermore, the current i(t) has an rms value of 10 A and leads v(t) by 90 degree(The current and the voltage have the same frequency.) What is the reactance of the load? is the load inductive or capacitive? I. -j1.06, inductive II. j1.06, inductive III. -j1.06, capacitive IV. j1.06, capacitive

Given Information:

Voltage = V(t) = 15cos(200πt + 65°)

Current = I(t) = 10 A rms

Required Information:

Reactance = X = ?

Reactance = 1.061 < -90° Ω

Reactance = -j1.061 Ω

Capacitive Reactance

Explanation:

The reactance is calculated by

X = V(t)/I(t)

V(t) = 15cos(200πt + 65°)

The voltage in polar form can be written as

V(t) = 15 < 65°

Where 15 is the magnitude and 65 is the phase angle

Convert the voltage to rms value

V(t) = 15/√2 < 65°

The current in polar form can be written as

I(t) = 10 < 65° + 90°

Since it was given that the current leads the voltage by 90°

I(t) = 10 < 155°

So the reactance is

X = V(t)/I(t)

X = (15/√2 < 65°)/(10 < 155°)

X = (15/10*√2 < 65° - 155°)

X = 1.061 < -90° Ω

or in rectangular form

X = -j1.061 Ω

Since the phase angle is negative, therefore, this is capacitive reactance.

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