Physics (Essay) Paper 2 WASSCE (SC), 2021

Question 11

 

(a)        (i)        What is meant by the root-mean-square value of an alternating current?
            (ii)       Define impedance of an alternating current circuit.
(b)        An electrical device rated 120 V, 60 W is operated on  a 240 V, 50 Hz mains supply. The circuit has a capacitor connected in series with the electrical device and the supply. Calculate the capacitance of the capacitor. [ = 3.142]
(c)        (i)        Define the capacitance of a capacitor.

            (ii)       

Observation

 

The circuit diagram above illustrates two capacitors of capacitance C1 and C2 connected in series across a 2 V sources.

  1. Obtain an expression for the total capacitance in terms of C2.
  2. Calculate the potential difference across each capacitor.

Part (a):     This was another popular question among the candidates. Most of the candidates failed to correctly provide the meaning of root-mean-square value of an a.c. current.

Part (b):     Performance was fair.

The expected responses:

(a)        (i)         Root-mean-square value

The direct current which has the same heating effect as the alternating current      

                     (ii)        Impedance of the circuit

The total opposition to the flow of an alternating current by both the resistive and reactive components.

                                    OR

The overall opposition of a circuit consisting of resistor, inductor and capacitor to the flow of alternating current in the circuit                                 

         (b)                                         

                                

                                                       

                                               
Vc = 207.85                            

                                 But Vc = IXc                                   

207.85 = 0.15 x  

C = 7,66μF                      

(c)        (i)         Definition of Capacitance of a Capacitor

                                 The charge per unit voltage on the plates                  

                     (ii)        (I)        Expression for Total Capacitance
                                            
                                    C1 and C2 are in series

                                    Total capacitance CT = C1C2             
C1+C2

                                                            Also C α 1                  
                                                d

                                   

                                   

 

                        (II)       Q = CTV                                

                                       =               

                                    V2 = Potential across C2

                                                V2 =                                     

                                                            

                                          = 1.43 V