Fundamentals ofElectric circuits

[Kokuson]

Homework Statement

The load in Fig. 11.44 draws 10 kVA at PF =0.8
lagging. If |IL |=40 A rms, what must be the value of C
to cause the source to operate at PF =0.9 lagging?

Homework Equations

P(apparent power VA)= |I| |V| cos@
@ = @V - @I
cos@= p.f
X= Xrms*(2)^0.5
S(complex power)= 0.5 * I * V (cos@ - j sin@)

The Attempt at a Solution

I just face a difficulty in knwoing the face of IL
I will be thankful if you solved the wole problem.

 

[rootX]

First, there is no capacitor. And, you have 10 kVA at 0.8 so 8 kW.

You add a capacitor and you get 10 kVA at 0.9 and 8KW

Find the reduction in the reactive power required to make the pf equal to 0.9. To find the capacitor value now you have its reactive power and you need voltage which is equal to the voltage across the source.

You can find the voltage across the source using the initial condition when there is no capacitor.

 

[Mene]

I am not able to provide a complete solution to this problem without more information. However, I can provide some guidance on how to approach the problem.

First, we need to understand the given information. The load in the circuit is drawing 10 kVA (kilovolt-amperes) at a power factor (PF) of 0.8 lagging. This means that the load is consuming a certain amount of reactive power, in addition to the active power. Reactive power is measured in units of volt-amperes reactive (VAR) and represents the power needed to create the magnetic field in inductive components in the circuit.

Next, we are given that the magnitude of the current, |IL|, is 40 A rms (root mean square). This means that the current is alternating at 40 A, and the rms value is the equivalent DC value that would produce the same amount of power in a resistive load.

To solve for the value of C, we need to use the equations for power in AC circuits. Specifically, we can use the equation P = |I| |V| cos@, where P is the active power, |I| is the magnitude of the current, |V| is the magnitude of the voltage, and @ is the phase angle between the current and voltage.

We know that the power factor is equal to cos@, so we can rearrange the equation to solve for @. Once we know @, we can use the equation @ = @V - @I to find the phase angle between the voltage and current.

Next, we can use the equation X = Xrms*(2)^0.5 to find the reactance of the circuit, where X is the reactance and Xrms is the rms value of the reactance. This will help us determine the value of the capacitor, C, needed to achieve a power factor of 0.9 lagging.

Finally, we can use the equation S = 0.5 * I * V (cos@ - j sin@) to calculate the complex power in the circuit, where S is the complex power, I is the current, V is the voltage, and j is the imaginary unit. This will help us verify that the circuit is operating at a power factor of 0.9 lagging.

Overall, the key to solving this problem is understanding the fundamentals of electric circuits and using the appropriate equations to solve for the unknown values