Question about RLC circuits

In summary, the conversation is about a person working near the secondary of a transformer and determining the rms voltage across their body. The secondary voltage is 6000V and the person's body resistance to ground is 1 Mega ohm. Using Ohm's law and integrating the current through the circuit, it is determined that the max voltage across the person's body is about 23 volts, with a corresponding current of 0.023 mA.
  • #1
andrew410
59
0
A person is working near the secondary of a transformer, as shown in the figure below. The primary voltage is 120 V at 60.0 Hz. The capacitance C, which is the stray capacitance between the hand and the secondary winding, is 10.0 pF. Assuming that the person has a body resistance to ground R, determine the rms voltage across the body. (Suggestion: Redraw the circuit with the secondary of the transformer as a simple AC source.)
FIGURE: http://east.ilrn.com/graphing/bca/user/appletImage?dbid=445132339 [Broken]

I need some help with this stuff. This is what I know already. I know that the secondary voltage is 6000 V according to the figure. Also, I know that the rms voltage = max voltage/sqrt(2). I'm not sure how to get the max voltage. I tried using the secondary voltage as the max voltage, but the answer wasn't right. So, I think the secondary voltage is the AC source. How do I get the max voltage using the secondary voltage? Maybe I'm doing this all wrong? I don't know...any help would be great! Thx in advance! :)
 
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  • #2
How about trying this? Let the voltage (secondary) as

[tex] v=v_0 e^{jwt}[/tex]

Find the current through the circuit i, using ohms law.

[tex] v_0 e^{jwt} = i (R_b -\frac{j}{wc})[/tex]

where -j/wc is the impedance of the capacitor.

Find the charge of the capacitor q by integrating current i since
i = dq/dt

use q= Cv to find the voltage across the capacitor [tex]v_c[/tex]

therefore, voltage across the body [tex]v_b = v - v_c[/tex]

absolute value of the vb is the max voltage created across the person's body. I am getting this to be about 23 volts using the human body resistance of 1 Mega ohm, causing a current of about 0.023 mA to flow through him. Hopefully it would not kill him. :rofl:
 
  • #3


Hi there,

First of all, let's redraw the circuit as suggested. We can simplify the secondary of the transformer as a simple AC source with a voltage of 6000 V. The stray capacitance C can be represented as a capacitor in parallel with the body resistance R, which is connected to ground.

Now, we can use the formula V = IZ to find the voltage across the body, where Z is the impedance of the circuit and I is the current flowing through it. We can find the impedance by using the formula Z = 1/(jωC + 1/R), where j is the imaginary unit and ω is the angular frequency (2πf).

So, plugging in the values we have, we get Z = 1/(j2π(60)(10x10^-12) + 1/R) = 1/(j0.012 + 1/R). Now, we need to find the current I. We can use Ohm's law, V = IR, to find the current. Since we know the voltage (6000 V) and the resistance (R), we can solve for I.

Finally, we can use the formula V = IZ to find the voltage across the body, which will give us the maximum voltage. We can then use the formula Vrms = Vmax/sqrt(2) to find the rms voltage across the body.

I hope this helps you understand how to approach this problem. Let me know if you have any further questions. Good luck!
 

1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor (R), an inductor (L), and a capacitor (C) connected in series or in parallel. These components interact with each other to regulate the flow of current and voltage in the circuit.

2. How does an RLC circuit work?

In an RLC circuit, the resistor limits the flow of current, the inductor stores energy in the form of a magnetic field, and the capacitor stores energy in the form of an electric field. The interaction between these components creates a resonant frequency at which the circuit can store and transfer energy most efficiently.

3. What are the applications of RLC circuits?

RLC circuits have a wide range of applications in various fields such as electronics, telecommunications, and power distribution. They are commonly used in filters, oscillators, amplifiers, and voltage regulators.

4. How do you calculate the resonance frequency of an RLC circuit?

The resonance frequency of an RLC circuit can be calculated using the formula f0 = 1/(2π√(LC)), where f0 is the resonance frequency, L is the inductance in henries, and C is the capacitance in farads.

5. What factors affect the impedance of an RLC circuit?

The impedance of an RLC circuit is affected by the values of the resistor, inductor, and capacitor, as well as the frequency of the input signal. Additionally, the type of circuit (series or parallel) and the configuration of the components can also affect the impedance.

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