Question

The potential across a $25.0\mu F$ capacitor is $5.0V$ What is the charge on the capacitor
(A) 0.20 microcoulombs
(B) 5.0 microcoulombs
(C) 125 microcoulumbs
(D) 30.0 microcoulombs
(E) We cannot determine the charge on the capacitor with the given information.

Answer 1

Capacitance is given and potential difference applied is given too so use to formula for charge stored when when certain voltage is applied across a certain capacitor or you can solve using basics, to do that you will have to assume certain charge on the plates of the capacitor then you will have to find the potential difference of the capacitor in terms of the assumed charge and then compare to get the answer.

Complete step by step answer:
We have, $capacitance = 25.0\mu F$ and remember capacitance is the capacity of a capacitor to hold a charge or it’s the ratio of charge on the capacitor to voltage across it. And be careful about the units, for example here the value of capacitance is given in microfarad if you will not consider that you might get the wrong answer.
$voltage = 5.0V$ ( it is given in the question and voltage in a capacitor is defined as ratio of charge on the capacitor and capacitance of the capacitor)
Using $Q = CV$ we have it’s the basic formula of the charge on capacitor and it says that charge stored in any capacitor is product of its capacitance and voltage across it
Charge stored $Q = 25.0 \times {10^{ - 6}} \times 5 = 125 \times {10^{ - 6}} = 125 micro\;coulombs$
Always be careful about the units like here potential difference is given in normal SI units but capacitance is given in micro units so if you will not be careful about the units else you might lose marks on your solution.

Hence Option-C is correct.

Note: In these type of questions don’t get confused by trying different things simply put the formula, you will get the answer and never forget to look for the units carefully like here capacitance is given in microfarad to charge will also come in the units of microcoulomb.