I think this will just about cover the net. ðŸ˜‰

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4.3 Principals of Circuits

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RC and RL time constants:

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RC â€“ R stands for Resistance and C stands for Capacitance. When a voltage is applied to a capacitor through a resistor in series, the capacitor begins to charge, it is not instantaneous. The time it takes to charge depends on the resistance and capacitance values. Think of the capacitor and the resistor as a water hose. The flow of water is limited by the size of the hose and the amount of water can be held is determined by the size of the bucket.

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In an RC circuit, the as the capacitor charges toward the value of the applied voltage, the current flowing decreases since the difference between the applied voltage and the capacitor charge decreases. **One time constant is defined as the time required for a capacitor to charge to 63.2% of the difference between the supplied voltage and the current charge on the capacitor. **If the capacitor is completely discharged, how long will it take for the capacitor to charge to 63.2% of the applied voltage? The formula for calculating a time constant is T = RxC. When a DC voltage is applied to a capacitor, it is considered fully charged after 5 time constants which is 99.3% of the applied voltage. In theory, the capacitor charge never equals the applied voltage, the difference just keeps decreasing by 63.2% each time constant.

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We can look at the charge as the remaining applied voltage after one time constant: 1.00 - .632 = .368 = 36.8% of the applied voltage is left â€“ the difference between the applied voltage and the charge on the capacitor.

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The time constant is consistent enough to be used in timing circuits. The famous (or infamous) 555 timer uses RC time constants.

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The discharge is calculated the same way. If a charged capacitor is placed in parallel with a resistor, the capacitor will begin do discharge through the resistor. The rate of discharge is one time constant. T = RxC. After one time constant 63.2% of the charged voltage will be discharged, leaving 36.8% of the voltage left on the capacitor. Again , after 5 time constants, the capacitor is considered discharged.

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E5B04 (D)

What is the time constant of a circuit having two 220 microfarad capacitors and two 1 megohm resistors, all in parallel?

A. 55 seconds

B. 110 seconds

C. 440 seconds

D. 220 seconds

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1)Â Â Â Â Â Â Â 2 1Mohm resistors in parallel = .5Mohms (500,000 ohms)R_{t }=

2)Â Â Â Â 2 220uf capacitors in parallel = 440uf (.00000000044 faradsÂ C_{t} = C_{1} + C_{2}

3)Â Â Â Â Tc = RxC = .5M x 440uf = 220 seconds (500000 x .00000000044)

IF the resistance is Mohms and the capacitance is uf, you can multiply them and the answer is in seconds. I find it easier to do them all in the power of 10 notation.

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(.5 x 10^{6}) x (440x10^{-6}) = 220 Â seconds

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This will work regardless of the unit multipliers.

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RL â€“ R stands for resistance and L stands for inductance. The capacitor above stores an electrostatic charge measured in voltage. It is like a battery that can discharge VERY quickly. An inductor stores energy in a magnetic field. Current flowing through the inductor causes a magnetic field to form and expand. The magnetic field is at right angles to the flow of the current. Then the conductor is wound into a coil the field in the adjacent coils combine forming an even stronger magnetic field.Â

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To visualize the way the magnetic fields form, we use a left-hand rule. Point your thumb along the conductor so that it points from the negative voltage polarity toward the positive voltage polarity then wrap your fingers around the conductor. Your fingers represent the magnetic field flow. IMPORTANT: This is electronic flow, negative to positive. If you are reading material using *Conventional flow*, this is a right-hand rule. The ARRL handbook and the question database is referring to the electronic flow.

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Remember that Capacitor and Inductors are opposites. The TC for a capacitor refers to voltage charge. The TC for an inductor refers to the flow of current. The current cannot change instantaneously.

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In the series RL circuit shown, the current will begin slowly and gradually increase. The TC is T=R/L. After one TC the current through the inductor will be 36.8% of the final maximum current and 68.2% is the difference between the final current and the present current â€“ the amount it will eventually increase. This is another example of how capacitors and inductors are opposite. Good news the numbers donâ€™t change. For memory, I try to just focus on the 63.2%. I can do the math for the other one.

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