A capacitor stores 10$\mu$C charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 20$\mu$C flows through the battery. The dielectric constant of the dielectric is

K = 3

The correct answer is Option 2: K = 3

$Q_1 = C V = 10 \ \mu C$

$C_2 = K C$

$Q_2 = C_2 V = K C V = 10K \ \mu C$

$\Delta Q = Q_2 - Q_1$

$20 = 10K - 10$

$10K = 30$

$K = 3$

The dielectric constant is $3$.