Capacitors in d.c. circuits
A capacitor is a gap in a A closed loop through which current moves - from a power source, through a series of components, and back into the power source. with space for Property of matter that causes a force when near another charge. Charge comes in two forms, positive and negative. For example, a negative charge causes a repulsive force on a neighbouring negative charge. on the 'plates' shown as the horizontal lines.
When a capacitor is charged, electrons on the lower plate repel Subatomic particle, with a negative charge and a negligible mass relative to protons and neutrons. from the upper plate, which then move to the positive terminal of the supply.
The The potential difference across a cell, electrical supply or electrical component. It is measured in volts (V). applied \(V_{c}\) to charge the capacitor (circuit 1 below) is measured with a A device used to measure potential difference or voltage.and charge accumulated \(Q\) is measured by removing the charged capacitor from circuit 1 and connecting it to a coulomb meter (circuit 2).
By varying the charging voltage and measuring the associated charge\(Q\) a graph can be drawn.
The gradient of this graph is equal to the capacitance of the capacitor.
\(C= \frac{Q}{V}\)
And the area under the graph is the energy stored by the capacitor.
\(E= \frac{1}{2}QV\)
This can be combined with the equation for capacitance above to give two alternative equations for energy stored.
\(E= \frac{1}{2}\frac{Q^2}{C}\) and
\(E= \frac{1}{2}C{V^2}\)
Question
A \(2200 \mu F\) capacitor is charged up with a \(1.5 V\) cell.
(a) What charge is stored?
(b) What energy is stored?
\(C= 2200\mu F\)
\(=2200 \times {10^{ - 6}}F\)
\(V = 1.5 V\)
\(Q=?\)
a) \(Q=CV\)
\(=2200 \times {10^{ - 6}} \times 1.5\)
\(=0.0033C\)
b) \(E= \frac{1}{2}C{V^2}\)
\(= \frac{1}{2} \times 2200 \times {10^{-6}} \times {1.5^2}\)
\(= 0.00248J\)