Capacitors in series Like other electrical elements, capacitors serve no purpose when used alone in a circuit. They are connected to other elements in a circuit in one of two ways: either in series or in parallel. In some cases it is useful to connect several capacitors in series in order to make a functional block: Analysis When this block is connected to a voltage source, each capacitor in the block stores an equal amount of charge, which means that the total amount of charge is evenly distributed across all of the capacitors, regardless of their capacitance. The amount of charge stored at each capacitor equals: where Qtotal is the total amount of charge in the complete block, and Q1 to Qn are charges at each individual capacitor. In order to explain why the charges at every capacitor are mutually equal, and equal to the total amount of charge stored in the complete series connection block, let us assume that all capacitors were uncharged at one point in time. When voltage is first applied across the block, the same current flows through all the capacitors and as a result, charge shift occurs. Electrons are carried from one plate of each capacitor to the other, which means that the charge stored by a plate of any of the capacitors must have come from the adjacent capacitor’s plate. This means that charge carriers (electrons) have simply shifted through all the capacitors, which is the reason that the charges at each capacitor are equal. That being said, it must be noted that the voltages across each capacitor are not equal, and are calculated for each capacitor by using the known formula: where Qn is the amount of charge on every capacitor in the series connection, Cn is the capacitance of the...
capacitors in series
What is inductance? Electric inductance is a property of all conductors. A change in the current flowing through the conductor creates (induces) a voltage in that conductor, as well as all nearby conductors. The induced voltage opposes the change in the current that induced the voltage. Inductance is a consequence of two laws of physics. Firstly, a constant current flowing through a conductor creates a constant magnetic field. Secondly, a variable magnetic field induces a voltage in all nearby conductors, including the conductor which was used to create the magnetic field in the first place. When these two laws are combined, the resulting effect is inductance. Just like resistors are used to introduce a desired resistance in a circuit, and like capacitors are used to introduce a desired capacitance, inductors are electrical elements used to introduce a desired amount of inductance into the circuit. The inductance formula for an ideal solenoid (a coil of wire) wound around a cylindrical body of material is given as: where L is the inductance, µ is the magnetic permeability of the material used in the inductor, A is the cross-sectional area of the coil and l is the length of the solenoid (not the length of the wire, but the longitudinal dimension of the coil). An ideal capacitor has no resistance and no inductance, but has a defined and constant value of capacitance. The unit used to represent inductance is henry, named after Joseph Henry, an American scientist who discovered inductance. Parasitic inductance Parasitic inductance is an unwanted inductance effect that is unavoidably present in all real electronic devices. As opposed to deliberate inductance, which is introduced into the circuit by the use of an inductor, parasitic inductance is almost always an undesired effect. There are few applications in which parasitic inductance is...