Question

(a) A capacitor has a value of 5 μF. Explain in terms of electric charge what this means. (b) The 5 uF capacitor shown in the circuit below is initially uncharged. The circuit is connected to a computer and switch S is closed. The monitor of the computer displays a graph of current against time as the capacitor charges monitoT charging current/uA 30 20 10 0 . 2,3 4 time s computer The battery has negligible internal resistance. (i) Calculate the resistance of R (ii) The resistor R, is replaced by another resistor R2. The resistance of R2 is half that of The capacitor is discharged and the experiment repeated. Sketch the graph of charging current against time when R2 is used. Include values on the axes. (c) In the following circuit a variable resistor R is used to keep the current constant as a different capacitor charges. The graphs on the monitor show how the charging current and р.d. across the capacitor vary with time after switch s is closed monitor 100 charging current time/s 10 capacitor time/s 10 0 computer (i) What adjustment must be made to the variable resistor R so that a constant charging current is produced? (ii) Show by calculation that 10 seconds after switch S is closed, the charge on the capacitor is 1mC (iii) Calculate the capacitance o of C

Answer 1

a) capacitor is a device which stores charge. When the battery is switched on, the current is stored as charge in the capacitor. once it is fully charged, charging is stopped. when the battery is removed, the capacitor is discharged i.e. the capacitor loses its charge.

b)

i) V = IR

R = V/I

= 6V/ 30 x 10 ^-6

=0.2 M ohms

ii) time constant = R x C

=  0.1 M ohms x 5 microfarad

= 0.5

Io = 39.3 micro A

therefore,

I = Io e^-t/RC

current vs time 45 40 35 30 25 20 15 10 4 0

c)

i)resistance should be decreased as the voltage increases gradually( to keep the current constant)