The amount of charge stored on a capacitor varies jointly as the voltage and area of the plates and inversely as the distance between the two plates of the capacitor. If a capacitor whose plates have area 16 and whose distance is apart and whose voltage is 25 stores 300 units of charge, how much charge does another capacitor hold if its plates have area 12 and distance apart and if its voltage is 28? Please show me the steps

Question

The amount of charge stored on a capacitor varies jointly as the voltage and area of the plates and inversely as the distance between the two plates of the capacitor.  If a capacitor whose plates have area 16 and whose distance is  apart and whose voltage is 25 stores 300 units of charge, how much charge does another capacitor hold if its plates have area 12 and distance  apart and if its voltage is 28?  Please show me the steps

mr.math · Answer

Lets write the charge $q$ as an expression of voltage $V$ , area of the plates $A$  and the distance between them $ d$,
$\large q={k VA \over d}$, where k is a constant.
Lets now substitute the values given in the first case,
$$300={k(25)(16) \over d} \implies {k \over d}={300 \over (25)(16)} \implies {k \over d}={3 \over 4}.$$
We can now try to find the charge with 12 units area plates, and voltage 28,
$$q={k \over d}VA={3 \over 4}(28)(12)=252 \text{ charge units}.$$

anonymous · Answer

Thanks