Resistor, capacitor and coil with Alternating current

In summary, the problem involves a circuit with a conduction coil, capacitor, and resistors. The voltage between the terminals of the conduction coil is found to be 49.4 Volts. The mistake in the calculation was due to rounding, and it is advised to use more significant digits during calculations.
  • #1
Karol
1,380
22

Homework Statement


A problem from a translated Sears-Zemansky, 1965, 14-10:
A conduction coil with inductance of 15 miliHenrys and resistance of 10 Ohms, is connected in line with a capacitor of 200 microFarads and a resistor of 12 Ohms.
The circuit is supplied with an alternating current of 100 Volts and frequency 50 cycles/sec.
What is the voltage between the terminals of the conduction coil?

Homework Equations


[tex]
\begin{equation*}
\begin{split}
\omega &=2\pi L \\
X_{L} &=\omega C \\
X_{C} &=\frac{1}{{\omega} C} \\
X &=X_{L}-X_{C} \\
Z &=\sqrt{R^{2}+X^{2}} \\
V_{active} &=I_{active}\times Z
\end{split}
\end{equation*}
[/tex]

The Attempt at a Solution



[tex]
\begin{equation*}
\begin{split}
X_{L} &=2\pi 50 \cdot 0.015=4.7 \\
X_{C} &=\frac{1}{2\pi 50 \cdot 2\times 10^{-4}}=15.9 \\
X &=4.7-15.9=-11.2 \\
Z &=\sqrt{22^{2}+(-11.2)^{2}}=24.7
\end{split}
\end{equation*}
[/tex]

The total active current in the circuit is found from the total active voltage equation:

[tex]100=I \cdot 24.7 \Rightarrow I=4.05[/tex]

The "Resistance" (I don't know how it is called in English, please tell me) Z on the conduction coil itself (with its resistance) is:

[tex]Z=\sqrt{R^{2}+X^{2}_L}=\sqrt{10^{2}+4.7^{2}}=11[/tex]

And the voltage on the coil is, using the total current in the circuit, calculated above:

[tex]V=I \times Z=4.05 \cdot 11=44.8[/tex]

The answer should be: 49.4 [Volts]
Where is the mistake?
Thanks-Karol
 

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  • #2
Your calculation is correct, but take care of rounding: use at least as many significant digits during the calculations as in the result.

ehild
 
  • #3
Thanks, I'l do that.
 

Related to Resistor, capacitor and coil with Alternating current

1. What is the purpose of a resistor, capacitor, and coil in an Alternating current circuit?

A resistor, capacitor, and coil are components commonly used in Alternating current (AC) circuits to control the flow and behavior of electricity. The resistor limits the amount of current flowing through the circuit, the capacitor stores and releases charge, and the coil creates a magnetic field that can induce current.

2. How do these components affect the behavior of Alternating current?

The resistor, capacitor, and coil all have different effects on the behavior of Alternating current. The resistor can control the amount of current flowing through the circuit, the capacitor can store and release charge, and the coil can create a magnetic field that can induce current. Together, these components can help regulate the flow of electricity and allow for the efficient transmission of AC power.

3. Can a circuit function without these components when using Alternating current?

Technically, a circuit can function without these components when using Alternating current. However, the behavior of the circuit may not be desirable or efficient. The resistor, capacitor, and coil are often used in AC circuits to regulate and control the flow of electricity, so their absence may result in an unstable or unpredictable circuit.

4. Are there any differences in using these components in an Alternating current circuit compared to a Direct current circuit?

Yes, there are differences in using these components in an Alternating current circuit compared to a Direct current circuit. In a DC circuit, the resistor, capacitor, and coil will behave differently due to the constant flow of electricity. In an AC circuit, the components must be designed to handle the changing direction and magnitude of the current. Additionally, the behavior of the circuit may differ due to the properties of AC and DC power.

5. How do engineers determine the appropriate values of these components for a specific Alternating current circuit?

The values of the resistor, capacitor, and coil are determined by the specific requirements and characteristics of the Alternating current circuit. Engineers will consider factors such as the desired current and voltage levels, the frequency of the AC power, and the properties of the components themselves to select the appropriate values. They may also use mathematical equations and simulations to optimize the performance of the circuit.

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