electrical circuits 2: Series RLC Circuit

Series RLC

A series RLC circuit.

The differential equation to a simple series circuit with a constant voltage source V, and a resistor R, a capacitor C, and an inductor L is:

$L\frac{d^2i}{dt^2} + R\frac{di}{dt} + {1 \over C}i = 0$

The characteristic equation then, is as follows:

$Ls^2 + Rs + {1 \over C} = 0$

With the two roots:

$s_1 = -{R\over 2L} + \sqrt{({R\over 2L})^2 - {1 \over LC}}$

and

$s_2 = -{R\over 2L} - \sqrt{({R\over 2L})^2 - {1 \over LC}}$

Series RLC

A series RLC circuit.

The differential equation to a simple series circuit with a constant voltage source V, and a resistor R, a capacitor C, and an inductor L is:

$L\frac{d^2i}{dt^2} + R\frac{di}{dt} + {1 \over C}i = 0$

The characteristic equation then, is as follows:

$Ls^2 + Rs + {1 \over C} = 0$

With the two roots:

$s_1 = -{R\over 2L} + \sqrt{({R\over 2L})^2 - {1 \over LC}}$

and

$s_2 = -{R\over 2L} - \sqrt{({R\over 2L})^2 - {1 \over LC}}$

SERIES RLC CIRCUITS

The principles and formulas that have been presented in this chapter are used in all ac circuits. The examples given have been series circuits.

This section of the chapter will not present any new material, but will be an example of using all the principles presented so far. You should follow each example problem step by step to see how each formula used depends upon the information determined in earlier steps. When an example calls for solving for square root, you can practice using the square-root table by looking up the values given.

The example series RLC circuit shown in figure 4-11 will be used to solve for X_L, X_C, X, Z, I_T, true power, reactive power, apparent power, and power factor.

The values solved for will be rounded off to the nearest whole number.

First solve for X_L and X_C.

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