Question

Touchscreens work on the principle of capacitance. In this problem, we want to think about what happens when you place a dielectric in a capacitor.

A. A parallel plate capacitor has one side attached to ground (V = 0), and the other side held at a fixed voltage of +V. What happens to the energy stored in the capacitor and the charge on the plates if I slide a sheet of plexiglass (dielectric constant κ ≈ 3) in between the plates?

The screen of your phone is made of a number of materials, including a plexiglass layer. Your hand is a pretty good conductor. When you touch your finger to the screen, it acts like the grounded plate of a capacitor, with internal pieces playing the roll of plates held at some (small) positive voltage.

B. How could the electronics detect when your finger gets very close to and touches the screen? That is, assuming the internal plates are held at a fixed voltage (which means they are attached to a battery), what could be changing inside your phone in a measurable way?

C. You’ve probably tried to use your phone when your finger is wet—it doesn’t work well! Given that water has a dielectric constant many times that of plexiglass (κwater ≈ 80), how could your answer to B help you explain why it doesn’t work?

Answer 1

A. Capacitance increases on introducing a dielectric. Energy stored is directly proportional to capacitance, hence it also increases.

Charge in presence of dielectric, Q_d = Q(1-1/k)= Q(1-1/3) = 2Q/3. ( where Q is charge of capacitor with vacuum or air as dielectric)

i.e. charge decreases.

B. As the finger touches the screen, the internal electric field inside the capacitor changes and this is how the device detect a touch.

C. Water is also a conductor. When we touch a screen with wet fingers, the water drops also change the internal electric field of the device, making it send confused signals to the circuit board. This is why the device can not function accurately if touched with wet hands.