Question

A 30-microfarad capacitor is charged to 90 v and then connected across an initially un charged capacitor of unknown capacitanc c .if the final potintial difference across the 30- microfarad capacitor is 20 v sitemin c

Answer 1

The value is
`C_u   =   5 *10^(-6) F`

Step-by-step explanation:

From the question we are told that

The voltage of the capacitor is
`V  =  90 \  V`

The capacitance of the capacitor is
`C  =  30 \ \mu F =  30 *10^(-6) \  F`

The final voltage is
`V_a =  20 \  V`

Since the capacitors are connected in parallel we have that

`Q_u  =  Q'_u  +  Q`

Where
`Q_u` is the charge of the known capacitor before it is connected to the known capacitor

`Q_u'` is the charge of the known capacitor after it is connected

`Q` is the charge of the unknown capacitor

Also the potential across the two capacitors will be the same (except for a loss due heat (it been converted to heat ))

So

`CV  =  CV_a +  C_u *  V_a`

=>
`C_u *  V_a   =  CV - CV_a`

=>
`C_u   =   (CV - CV_a )/( V_a )`

=>
`C_u   =   ( [30*10^(-6) *90] - [30*10^(-6) * 20] )/( 20 )`

=>
`C_u   =   5 *10^(-6) F`