Is the Solution to the Equivalent Impedance Problem Correct?

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In summary, an equivalent impedance problem is a circuit analysis problem where the goal is to determine the total impedance of a circuit by combining different components. It is important to solve these problems to understand circuit behavior and design. The method for calculating equivalent impedance depends on the type of circuit and involves using complex numbers for components like capacitors and inductors. These problems can be solved manually or using software, but understanding the manual method is crucial for a deep understanding of the concepts.
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ness9660
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Given this problem and its solution:

http://img230.imageshack.us/img230/9239/quest13lf.gif


I think the given solution is wrong. The equivalent impedence is R + jwL || 1/jwC, right?

When I work out jwL || 1/jwC, I get ((jwL) * (1/jwC))/ (jwL + 1/jwC) = jwL / (j(w^2)CL + 1).


However the given solution has 1- j(w^2)CL instead of my 1 +.

Ive worked this out every way I could think of, is the given solution correct, or am I correct?
 
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Nevermind, I feel dumb now.

I completely missed that j^2=-1
 
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The given solution appears to be incorrect. The correct equivalent impedence should be 1/(jwC + 1/(jwL)) or (jwL)/(jwL + 1/(jwC)). The equation provided in the solution, 1-j(w^2)CL, does not match either of these forms. It is important to double check solutions to ensure accuracy in scientific calculations.
 

FAQ: Is the Solution to the Equivalent Impedance Problem Correct?

What is an equivalent impedance problem?

An equivalent impedance problem refers to a circuit analysis problem where the goal is to determine the total impedance of a circuit. This involves combining different resistors, capacitors, and inductors in series or parallel to find the equivalent impedance.

Why is solving equivalent impedance problems important?

Solving equivalent impedance problems is important because it allows us to understand how a circuit will behave when different components are connected in a specific way. It also helps in designing circuits and predicting their performance.

How do you calculate equivalent impedance?

The method for calculating equivalent impedance depends on the type of circuit being analyzed. For resistors in series, the equivalent impedance is the sum of all the individual resistances. For resistors in parallel, the equivalent impedance is the reciprocal of the sum of the reciprocals of the individual resistances. For capacitors and inductors, the equivalent impedance is calculated using the same rules as resistors but with the use of complex numbers.

What is the significance of complex numbers in equivalent impedance problems?

Complex numbers are used in equivalent impedance problems because they allow us to take into account the effects of capacitance and inductance on the circuit. These components introduce a phase difference between the voltage and current, which can only be accurately represented using complex numbers.

Can equivalent impedance problems be solved using software or must they be done manually?

Equivalent impedance problems can be solved both manually and using software. While manual calculations may be more time-consuming and prone to errors, software programs and online calculators can provide quick and accurate solutions. However, it is important to understand the manual method in order to fully grasp the concepts behind equivalent impedance problems.

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