Electricity doesn’t enter your finger, but rather your finger has its own charges. Your finger acts as what’s called a dielectric. Basically, it interferes with the electric field across the capacitor, changing the capacitance, which means the capacitor can hold more charge, so some current flows. That flow of current is what the screen interprets as touch.
C=Q/V
C=εA/d
C is capacitance, Q is charge, V is voltage
ε is the electrical permittivity of the dielectric, ε_0 specifically is the permittivity of free space and a dielectric will increase that.
A is the area of the two plate of the capacitors (which doesn’t change) and d is the distance between those plates (which also doesn’t change
Since we only change ε, C changes. The voltage of the circuit doesn’t change, so since C changed, the charge must change. For charge to change, it requires a current (I = dQ/dt)
Latest Answers