Solving voltage divider involving capacitors

In summary, to find VV/VC, you need to use Kirchoff's laws and check your arithmetic. The voltage through ZV1, ZV2, and CV is the same (VV). You can also use the equation 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV to solve for ZV and then use it to find VV/VC. Make sure to double check your calculations.
  • #1
wu_weidong
32
0

Homework Statement


2cymnon.png

Given ZV1 = ZV2 = 100Ω,
ZCCV = ZCV = 2000/j = -2000j, and
VV/VC = 0.04789.

I'm trying to get the given VV/VC result.

Homework Equations


I know that
1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV
VV = ZV / (ZV + ZCCV) * VC

The Attempt at a Solution


1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV = 1/100 + 1/100 + j/2000
|1/ZV| = √(0.022 + (1/2000)2) = 0.02
ZV = 50Ω

VV/VC = ZV / (ZV + ZCCV) = 50 / (50 - 2000j)
VC/VV = (50 - 2000j) / 50 = 1 - 40j
|VC/VV| = √(12 + 402) = 40.01
VV/VC = 1/40.01 = 0.02499
which is about half of the value I should get.

Where did I go wrong?
 
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  • #2
Kirkoffs laws - check arithmetic.
 
  • #3
Simon Bridge said:
Kirkoffs laws - check arithmetic.
Can I please have a bit more hint?

The voltage through ZV1, ZV2 and CV is the same (VV), right?
 

Related to Solving voltage divider involving capacitors

1. How do I calculate the equivalent capacitance in a voltage divider involving capacitors?

To calculate the equivalent capacitance in a voltage divider, you can use the formula Ceq = C1 + C2 + ... + Cn, where C1, C2, and Cn represent the individual capacitances in the circuit. Alternatively, if the capacitors are in series, you can use the formula 1/Ceq = 1/C1 + 1/C2 + ... + 1/Cn. If the capacitors are in parallel, you can simply add their values together to find the equivalent capacitance.

2. How do I determine the voltage across each capacitor in a voltage divider?

To determine the voltage across each capacitor in a voltage divider, you can use the formula Vc = Vtot * (Cn / Ceq), where Vc is the voltage across the specific capacitor, Vtot is the total voltage in the circuit, Cn is the capacitance of the specific capacitor, and Ceq is the equivalent capacitance of the circuit.

3. Can I use the voltage divider rule for capacitors?

Yes, the voltage divider rule can be used for capacitors in a circuit. This rule states that the voltage across a specific component is proportional to its resistance (or in this case, capacitance) compared to the total resistance (or equivalent capacitance) in the circuit. This can be expressed as Vc = Vtot * (Rn / Req) or Vc = Vtot * (Cn / Ceq).

4. What is the purpose of using a voltage divider with capacitors?

The purpose of using a voltage divider with capacitors is to divide the input voltage into smaller, manageable voltages. This can be useful in electronic circuits where precise voltage levels are required for different components. It also allows for the use of capacitors with different values to achieve specific voltage ratios.

5. Can I use the same formula for a voltage divider involving capacitors and resistors?

No, the formula for a voltage divider involving capacitors is different from the formula for a voltage divider involving resistors. In a voltage divider with resistors, the voltage across each resistor is proportional to its resistance compared to the total resistance in the circuit. This can be expressed as Vr = Vtot * (Rn / Req). As mentioned earlier, in a voltage divider with capacitors, the voltage across each capacitor is proportional to its capacitance compared to the equivalent capacitance in the circuit.

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