Answers to Problems - The Capacitor

1. What is the charge stored when the voltage across a 50 μF capacitor is 9 V?
   
   

   Q  =  VC  =  9 V  ×  50 μF  =  450 μF

2. What is the capacitance of a capacitor that stores 12 μC of charge when connected to a 6 V battery?
   
   

   C  =	Q	=	12 μC	=  2 μC
   	V		6 V

   
   
   
3. Work out the voltage across the plates of a 10 μF capacitor when it has a charge of 50 μC.
   
   

   V  =	Q	=	50 μC	=  5 V
   	C		10 μF

   
   
   
4. Calculate the energy stored in a capacitor with a charge of 200 μC and 9 V across its plates.
   
   

   W  =  ½ QV  =	200 μC  ×  9 V	=  0.9 mJ
   	2

   
   
   
5. Calculate the energy stored in a 1 μF capacitor charged to 50 V.
   
   

   W  =  ½ V 2C  =	2500 V  ×  1 mF	=  1.25 mJ
   	2

   
   
   
6. What is the combined capacitance of:
   
   a) a 2.2 μF capacitor and a 4.7 μF capacitor in parallel?
   

   C_TOTAL  =  C₁  +  C₂  =  2.2 μF  +  4.7 μF  =  6.9 μF

   b) two 100 μF capacitors in series?
   
   

   CTOTAL  =	C1  ×  C2	=	10,000 μF	=  50 μF
   	C1  +  C2		200 μF

   
   
   
7. What is the total combined capacitance of the network shown below?
   
   
   
   
   

   CTOTAL  =	C1  ×  (C2  +  C3)	=	5 μF  ×  25 μF	=  4.167 μF
   	C1  +  (C2  +  C3)		30 μF