Leakage Resistance of a Capacitor
The resistance of the dielectric of the capacitor is called the leakage resistance of a capacitor. The dielectric in an ideal capacitor is a perfect insulator (i.e., it has infinite resistance) and zero current flows through it when a voltage is applied across its terminals.
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The dielectric in a real capacitor has a large but finite resistance so a very small current flows between the capacitor plates when a voltage is applied.
The above figure shows the equivalent circuit of a real capacitor consisting of an ideal capacitor in parallel with leakage resistance Rl. Typical values of leakage resistance of a capacitor may range from about 1 MΩ (considered a very “leaky” capacitor) to greater than 100,000 MΩ. In a well-designed capacitor, the leakage resistance of a capacitor is very high (> 104 MΩ) so very little power is dissipated even when high voltage is applied across it.
Factors affecting Leakage resistance
- Temperature: The leakage resistance of a capacitor normally decreases with the increase in temperature.
- Potential stress: High voltage increases the leakage current by decreasing the leakage resistance of a capacitor.
- Size of the capacitor: Smaller capacitor tends to have more leakage currents due to increased electric field strength. Hence, it can be said that the smaller the size, the lower will be the leakage resistance of a capacitor.
- Dielectric material: The leakage resistance of a capacitor also varies with the selection of dielectric material.
Voltage Rating of a Capacitor
The maximum voltage that may be safely applied to a capacitor is usually expressed in terms of its DC working voltage.
The maximum DC voltage that can be applied to a capacitor without a breakdown of its dielectric is called the voltage rating of the capacitor.
If the voltage rating of a capacitor is exceeded, the dielectric may break down and conduct current, causing permanent damage to the capacitor. Both capacitance and voltage ratings must be taken into consideration before a capacitor is used in a circuit application.
Capacitors in Series
Consider three capacitors, having capacitances C1, C2, and C3 farad respectively, connected in series across a potential difference of V volts. In a series connection, the charge on each capacitor is the same (i.e. +Q on one plate and −Q on the other) but the potential difference across each is different.
Now, V = V1 + V2 + V3 = Q/C1 + Q/C2 + Q/C3
= Q (1/C1 + 1/C2 + 1/C3)
Or, V/Q = (1/C1 + 1/C2 + 1/C3)
But Q/V is the total capacitance CT between points A and B so that V/Q = 1/CT
1/CT = (1/C1 + 1/C2 + 1/C3)
Thus, capacitors in series are treated in the same manner as resistors in parallel.
When voltage V is applied, a similar electron movement occurs on each plate. Hence the same charge is stored by each capacitor. Alternatively, the current (charging) in a series circuit is the same. Since Q = It and both I and t are the same for each capacitor, the charge on each capacitor is the same.
Total or equivalent capacitance is the single capacitance which if substituted for the series capacitances, would provide the same charge for the same applied voltage.
The capacitors are connected in series when the circuit voltage exceeds the voltage rating of individual units. In using the series connection, it is important to keep in mind that the voltages across capacitors in a series are not the same unless the capacitances are equal. The greater voltage will be across the smaller capacitance which may result in its failure if the capacitances differ very much.
Capacitors in Parallel
Consider three capacitors, having capacitances C1, C2, and C3 farad respectively, connected in parallel across a potential difference of V volts. In a parallel connection, the potential difference across each capacitor is the same but the charge on each is different.
Here, Q = Q1 + Q2 + Q3 = C1 V + C2 V + C3 V
= V (C1 + C2 + C3)
or Q/V = C1 + C2 + C3
But Q/V is the total capacitance CT of the parallel combination
CT = C1 + C2 + C3
Thus, capacitors in parallel are treated in the same manner as resistors in series. Capacitors may be connected in parallel to obtain larger values of capacitance than are available from individual units.
