Question

Two parallel plate capacitors X and Y are connected in series to a 6 V battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant 4. Calculate the capacitances of X and Y, if the equivalent capacitance of the combination of X and Y is \(4\,\mu\text{F}\).

Hint:

If two identical capacitors differ only by dielectric constant \(K\), then \[ C_{\text{dielectric}}=K\,C_{\text{air}}. \] For capacitors in series, \[ C_{\text{eq}}=\frac{C_1C_2}{C_1+C_2}. \]

Answer 1