FIGURE 2.4 below shows a parallel RLC circuit that consists of a 75 Ω resistor, an inductor with unknown inductance value and a capacitor with a capacitive reactance of 50 Ω, all connected across a 300 V AC supply voltage. The current flowing through the resistor is 4 A and the current flowing through the inductor is 3 A. Answer the questions that follow. 1. Calculate the value of the current through the capacitor. 2. Calculate the value of the inductive reactance. 3. Calculate the value of the total current. 4. Calculate the phase angle.

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FIGURE 2.4 below shows a parallel RLC circuit that consists of a 75 Ω resistor, an inductor with unknown inductance value and a capacitor with a capacitive reactance of 50 Ω, all connected across a 300 V AC supply voltage - English General - NSC Electrical Technology: Power Systems - Question 2 - 2021 - Paper 1

Question 2

FIGURE 2.4 below shows a parallel RLC circuit that consists of a 75 Ω resistor, an inductor with unknown inductance value and a capacitor with a capacitive reactance... show full transcript

Worked Solution & Example Answer:FIGURE 2.4 below shows a parallel RLC circuit that consists of a 75 Ω resistor, an inductor with unknown inductance value and a capacitor with a capacitive reactance of 50 Ω, all connected across a 300 V AC supply voltage - English General - NSC Electrical Technology: Power Systems - Question 2 - 2021 - Paper 1

Step 1

Calculate the value of the current through the capacitor.

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Answer

To find the current through the capacitor ( $I_C$ ), we can use Kirchhoff's Current Law which states that the total current entering a junction equals the total current leaving the junction.

Let:

$I_T = I_R + I_L + I_C$
Given:
- $I_R = 4 ext{ A}$ (current through the resistor)
- $I_L = 3 ext{ A}$ (current through the inductor)

Thus, we can rearrange it as follows:

$I_C = I_T - I_R - I_L$

Substituting the values, we need to find $I_T$ first:

$I_T = I_R + I_L + I_C$ (Using the given values, we can estimate $I_C$ )

This leads to $I_T = 4 + 3 + I_C = I_T$ .

Using the provided currents: $I_T = 4 + 3 = 7 ext{ A}$

Now substituting back: $I_C = 7 - 4 - 3 = 0 ext{ A}$

So, the capacitor carries no current, or $I_C = 0 ext{ A}$ .

Step 2

Calculate the value of the inductive reactance.

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Answer

To find the inductive reactance ( $X_L$ ), we can use the formula:

$X_L = rac{V}{I_L}$

Where:

$V = 300 ext{ V AC}$
$I_L = 3 ext{ A}$

Thus: $X_L = rac{300}{3} = 100 ext{ Ω}$

So, the inductive reactance is $X_L = 100 ext{ Ω}$ .

Step 3

Calculate the value of the total current.

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Answer

The total current in the circuit is already calculated through the previous steps. By summing up the components:

$I_T = I_R + I_L$ where:

$I_R = 4 ext{ A}$
$I_L = 3 ext{ A}$

Thus: $I_T = 4 + 3 = 7 ext{ A}$

Hence, the total current flowing in the circuit is $I_T = 7 ext{ A}$ .

Step 4

Calculate the phase angle.

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Answer

The phase angle ( $heta$ ) in a parallel RLC circuit can be calculated using:

$heta = ext{arccos}igg( rac{I_R}{I_T}igg)$

We have:

$I_R = 4 ext{ A}$
$I_T = 7 ext{ A}$

Substituting the values:

$heta = ext{arccos}igg( rac{4}{7}igg)$

Calculating this:

Use a calculator to find $ext{arccos}(0.5714)$ .
This yields approximately $heta ightarrow 55.0^{ ext{o}}$ .

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