Capacitance 2

Recall the definition of capacitance

Write down the equation for capacitance.

If we were to plot the graph of charge against potential difference, what would the graph look like? Will it be straight or a curve? Recall the equation of a straight line: y = mx + c

• Straight line

• Curve

Sketch the graph of charge against potential difference. Think which quantity should be on the y-axis and which should be on the x-axis.

Answer explanation

hint: can you rearrange it into a straight line equation?

Write down the formula for gradient using the quantities you have plotted on the graph.

So what can you deduce about the gradient of the charge against potential difference graph in relation to its capacitance?

Answer explanation

Equation for gradient = Q/V = Capacitance.

Therefore, we can deduce that the gradient = capacitance.

The energy stored in the capacitor is equal to the area under the graph of charge against potential difference. Write down the formula for area under the graph.

Answer explanation

Graph should have been a straight line. Hence the area under the graph is a triangle. Area of triangle is 1/2 x base x height. So applying this formula will give the area = 1/2 x Q x V.

Using the equation Q = CV, derive another equation for energy stored.

Using the equation, V = Q/C derive another equation for energy stored in a capacitor

State all the equations for energy stored in a capacitor.