How to Calculate Voltage Drop Across a Capacitor

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A capacitor consists of two conductors separated by a vacuum or dielectric. A common geometrical configuration uses parallel plate conductors, another arrangement is a concentric cylinder. When charges of equal and opposite sign are placed on the conductors an electric field forms in the region between the plates, resulting in a potential difference V across them. The magnitude of this voltage drop is given by the formula V=Q/C Volts, where Q is the charge on the plates and C is the capacitance.

How to Calculate Voltage Drop Across a Capacitor

  • Get the capacitance. For the special case of a parallel plate capacitor this is given by the formula C=epsilon0*A/d Farads, where epsilon0 is the permittivity of free space or a vacuum with a value of 8.854e-12 C^2/NM^2, A is the area across the face of the conductors and d is the distance between the plates.

  • Determine the dielectric constant K, if the conductors are separated by a nonconducting material. A dielectric material has the effect of increasing the capacitance and decreasing the voltage. The dielectric constant is a measure of the extent to which the dielectric modifies the capacitor’s parameters. In general, the capacitance becomes Cd=KC and the voltage decreases to Vd=V/K, where C and V are the values of the capacitance and voltage in a vacuum, respectively. The dielectric can be accounted for in a parallel plate capacitor by replacing epsilon0 in the equation for the capacitance by the permittivity of the dielectric epsilonD=Kepsilon0. Common values of the dielectric constant at 20 degrees Celsius are K=1 for teflon, k=3.1 for mylar, and and K=5 to 10 for glass.

  • Calculate the voltage drop using the formula V=Q/C. For example, if a parallel plate capacitor has a vacuum between its plates with a charge of 100 microcoulombs and a capacitance of 10 microfarads then the voltage is V=10 Volts. If a dielectric, with a dielectric constant of K=5, is inserted in between the plates the capacitance Cd becomes Cd=K*C=50 microfarads and the voltage Vd decreases to Vd=V/K=2 Volts.

Tips & Warnings

  • The arrangement of capacitors in circuits can affect the voltage drop across them. In a series connection the magnitude of the charge on all the plates is the same giving different voltages across the elements that are inversely proportional to the capacitance of each capacitor. In a parallel connection the voltage drop across all the capacitors is the same.
  • Photo Credit capacitor image by Albert Lozano from Fotolia.com
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Resources

  • ‘Fundamentals of Physics’;D Halliday, R Resnick and J Walker;2001

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