### Series and Parallel Inductors | Inductors | Electronics Textbook

The voltage drop across all of the inductors in parallel will be the same. through each inductor in our circuit above, and substituting the current i for i1 + i2 + i3 the voltage across the By substituting di/dt in the above equation with v/L gives: . Ohm's Law; Capacitor and Inductor Response; Filters; Operational Amplifiers. Since the current through each parallel inductor will be a fraction of the total current, and the voltage across each parallel inductor will be equal, a change in total. We can prove the equation for parallel resistors by using Kirchhoff's voltage and current laws.

Resistors As the current flows through the resistors, in the same way that water flows over rocks, it expends some of its energy. If the rocks in a stream were in the form of rapids, the stream would have considerable resistance.

### Voltage vs. Current in a Resistor, Capacitor or Inductor

However, if the same amount of rocks were placed in a row across the stream, the overall resistance to current flow would be less. The diagrams below illustrate the basic but underlying principle in the majority of electrical systems.

In the series circuit on leftthe same current flows through every resistor, but the applied voltage isdivided between them.

In the parallel circuit on rightthe same voltage is applied to all resistors but the current divides between them. Circuits containing a combination of series and parallel portions apply the same basic theory with more lengthy calculations. Capacitors A capacitor, as previously described, is physicallymade of two conducting surfaces separated by an insulator.

## Resistors (Ohm's Law), Capacitors, and Inductors

Due to Faraday's lawthe EMF which drives the current is caused by a decrease in the magnetic field, thus the energy required to charge the capacitor is extracted from the magnetic field. When the magnetic field is completely dissipated the current will stop and the charge will again be stored in the capacitor, with the opposite polarity as before.

Then the cycle will begin again, with the current flowing in the opposite direction through the inductor. The charge flows back and forth between the plates of the capacitor, through the inductor.

The energy oscillates back and forth between the capacitor and the inductor until if not replenished from an external circuit internal resistance makes the oscillations die out. In most applications the tuned circuit is part of a larger circuit which applies alternating current to it, driving continuous oscillations.

**AC current impedance - Alternating Voltage for inductors, capacitors**

The tuned circuit's action, known mathematically as a harmonic oscillatoris similar to a pendulum swinging back and forth, or water sloshing back and forth in a tank; for this reason the circuit is also called a tank circuit. In typical tuned circuits in electronic equipment the oscillations are very fast, from thousands to billions of times per second. With the exception of equations dealing with power Pequations in AC circuits are the same as those in DC circuits, using impedances Z instead of resistances R.

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KVL tells us that the algebraic sum of the voltage drops across the resistor, inductor, and capacitor should equal the applied voltage from the source. Even though this may not look like it is true at first sight, a bit of complex number addition proves otherwise: Aside from a bit of rounding error, the sum of these voltage drops does equal volts. As you can see, there is little difference between AC circuit analysis and DC circuit analysis, except that all quantities of voltage, current, and resistance actually, impedance must be handled in complex rather than scalar form so as to account for phase angle.

The only exception to this consistency is the calculation of power, which is so unique that it deserves a chapter devoted to that subject alone.

## Series and Parallel Inductors

Impedances of any kind add in series: Zn Although impedances add in series, the total impedance for a circuit containing both inductance and capacitance may be less than one or more of the individual impedances, because series inductive and capacitive impedances tend to cancel each other out.

This may lead to voltage drops across components exceeding the supply voltage! All rules and laws of DC circuits apply to AC circuits, so long as values are expressed in complex form rather than scalar.