What is the Voltage Across the Capacitor in an RLC Circuit with Zero Inductance?

In summary, the inductance in the RLC circuit is 0 and the generator and resistor have rms voltages of 45V and 24V respectively. Using the equations Vrms= Vmax/ Sq rt 2 and V c = IX c, it can be calculated that the voltage across the capacitor is 16V. This can also be determined using Kirchoff's voltage law by calculating the sum of voltages across all three elements in the loop to be 0.
  • #1
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Homework Statement



The inductance is 0 in the RLC Circuit. the rms voltage across the genreator and the resistor are 45, and 24V. Wats the voltage across the capacitor?

Homework Equations



Vrms= Vmax/ Sq rt 2
V c = IX c ,

The Attempt at a Solution



V= I/R
I= V/R 24/45= 8/15A

C can be calculated since there's no F or L
 
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  • #2
Recall the Kirchoff's voltage law. The voltage across all elements in a loop added is zero. Here there are only three elements ( generator, resistor and capacitor). The sum of voltages across them should be zero. You know voltage across two elements. Hence it is easily to calculate the voltage across C directly.
 

1. What is RMS voltage across a capacitor?

The root mean square (RMS) voltage across a capacitor is the effective voltage that produces the same amount of heat as a direct current (DC) voltage. It takes into account the effects of AC voltage and the varying capacitance of the capacitor.

2. How is RMS voltage calculated across a capacitor?

To calculate the RMS voltage across a capacitor, you need to know the peak voltage (Vp) and the capacitance (C) of the capacitor. The formula is Vrms = Vp / √2, where √2 is the square root of 2.

3. Why is it important to know the RMS voltage across a capacitor?

Knowing the RMS voltage across a capacitor is important in determining the power and energy consumption of an electrical circuit. It also helps in selecting the appropriate capacitor for a specific application.

4. How does the frequency affect the RMS voltage across a capacitor?

The frequency of the AC voltage has a direct impact on the RMS voltage across a capacitor. As the frequency increases, the capacitor's reactance decreases, resulting in a higher RMS voltage. Conversely, a decrease in frequency leads to a lower RMS voltage.

5. Can the RMS voltage across a capacitor be higher than the peak voltage?

Yes, the RMS voltage across a capacitor can be higher than the peak voltage in some cases. This occurs when the AC voltage has a non-sinusoidal waveform, such as a square wave or a triangle wave, which have higher RMS values compared to their peak values.

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