Capacitors in series and parallel Anushka Saxena, XII SD
CONTENTS Certificate Acknowledgement Objective Capacitor and capacitance Principle of capacitor Capacitors in series Capacitors in parallel Mathematical comparison Material required The Circuit How to operate Observation and Conclusion
Certificate This is to certify that ANUSHKA SAXENA of class XII Springdale has worked on the project “Capacitors in series and parallel” to my full satisfaction
Date
Signature ( Sakshi Katyal)
It is a pleasure to acknowledge many people who knowingly helped me complete my project. First and foremost, I would like to express my regards towards Sakshi Katyal, the honorable teacher of my school for her encouragement and guidance. I would also like to express my immense gratitude towards Himanee Datta, my partner for providing the invaluable cooperation and support extended during the completion of this project. (Anushka Saxena)
Objective To study and compare the behavior of capacitors in parallel and series combination.
Capacitor and capacitance Capacitor is an electrical device that can store energy in the electric field between a pair of closely spaced conductors(called 'plates'). When current is applied to the capacitor, electric charges of equal magnitude, but opposite polarity, build up on each plate. Capacitors are used in electrical circuits as energy-storage devices. Capacitance is ability of a conductor to store electric charge or energy is known as electrical capacitance of the conductor. when a charge is given to a conductor, it is raised to certain potential. More the charge on the conductor, higher is it’s potential. Q � V where Q Is the charge given to the conductor and V is it’s electric potential Q=CV, where C is the constant of proportionality called capacitance C= Q/V Unit : Farad
Principle of capacitor When a charged conductor is placed near an uncharged conductor, the potential of the charged conductor falls. To raise the conductor to the initial potential, more charges can be added.
Capacitors in series Electrons move from –ve to +ve ( By convention -> +ve to –ve) terminal of battery. Electrons start collecting on the right side on the right side of capacitor C₃, the right plate gets negatively charged. This negatively charged plate induces +ve chare on the opposite plate (left plate). Hence the right plate of C₂ gets same charge as the same amount of electrons have moved from C₂ right plate to the C₃ left plate. Hence same amount of charge in each capacitor. Potential across each capacitor is different. This can be explained by a simple analogy : Suppose there is a stationary source charge and few charges near it, the charge closer to source would be at higher potential than the one away from source. If you draw a line from the source, at each point there will be a different potential. See the illustration below for better understanding. V₁= Q/C₁ , V₂=Q/C₂ , V₃ =Q/C₃ V=V₁+V₂+V₃ V= Q/C Q/C = Q/C₁ + Q/C₂ + Q/C₃
+
=> 1/Cs = 1/C₁ + 1/C₂ + 1/C₃
Capacitors in parallel
Contrary to series potential is same across each capacitor in case of parallel.
Q₁= VC₁ , Q₂=VC₂ , Q₃ =VC₃ Q=Q₁+Q₂+Q₃ = Cp V
As current flows, the charge is being distributed in the three wires connected to parallel capacitors.
CpV = VC₁ +VC₂ +VC₃
Hence charge in each capacitor is different in parallel combination
Cp= C₁ +C₂ +C₃
Mathematical comparison… Cp= C₁ +C₂ +C₃ 1/Cs = 1/C₁ + 1/C₂ + 1/C₃
Cs = ( C₁ +C₂ +C₃ ) / ( C₁ C₂ C₃ ) Hence, it is self explanatory that
Cp > Cs .
Capacitances diminish in series. Capacitances add in parallel.
Material Required
THE CIRCUIT The circuit is simply a two transistor direct coupled amplifier. The key provides the base voltage to T1 via R1 resistor. The collector gives voltage to LED through its collector. The using of two transistor is to draw lesser current and to increase on time of LED at the output. The resistor R2 provides excess charge current at t1 base. The probes senses the combination of capacitors, either it is parallel or series, and provides charge on time to the T1 base and finally for the on time LED.
HOW TO OPERATE? To operate circuit for any one of the combination, connect wiring sequence as given and also connect capacitor in either series or parallel combination. Now connect capacitor in either series or parallel combination. Now connect the probe to the combination terminals and charge the capacitor by pressing the key for few seconds. Release the key and take reading (in seconds) the total time to discharge these through circuit. The output is displayed in form of LED’s light.
OBSERVATION : Time taken in parallel combination : Time taken in series combination : CONCLUSION : It is clear from our experiment that the parallel combination will take more time to discharge in comparison to series combination for two equal value capacitors.
Bibliography 1. Fundamentals of physics By Haliday Resnick Walker 2. Class 12 Physics textbook(NCERT) 3. Youtube.com/rimstar.org