The Theory Of Capacitor’s Power

Introduction: 

Every electrical device has a fixed rate of work. The rate of work is called power. An electrolytic capacitor has its own power. Here I will discuss about the power of electrolytic capacitor. 

Abstract:  

Every electrical device has a ability of work. The rate of work is called power. Here we will discuss about the power of capacitor.

Method:  

I have invented a formula to determine the value of power of electrolytic capacitor. Here’s the method-

We know that- W= ½CV²

                           = ½C×(Q÷C)²

                           = Q²÷2C

So, W= Q²÷2C________(i)

Again, we know that- P= W÷t

                                     = Q²÷(2C×t)

                                     = Q×Q÷2C×t

                                     = IQ÷2C

So, P= IQ÷2C_________(ii)

If IQ= 2IQ then-

P'= 2IQ÷2C

   = 2(IQ÷2C)

   = 2P

So, P'= 2P

Again, If IQ= ½IQ then-

P'= ½IQ÷2C

   = ½(IQ÷2C)

   = ½P

So, P'= ½P

If the value of capacitor’s charge and electric conduction increases, then the value of capacitor’s power increases proportionally. If the value of capacitor’s charge and electric conduction decreases, then the value of capacitor’s power decreases proportionally. 

So, P∞ IQ_________(iii)

If C= 2C then-

P'= IQ÷2(2C)

   = IQ÷4C

   = ½(IQ÷2C)

   = ½P

So, P'= ½P

If C= ½C then- 

P'= IQ÷2(½C)

   = 2IQ÷2C

   = 2(IQ÷2C)

   = 2P

So, P= 2P

If the value of capacitor’s capacitance increases, then the value of capacitor’s power decreases disproportionally. If the value capacitor’s capacitance decreases, the value of capacitor’s power increases disproportionally. 

So, P∞ 1÷C_________(iv)

The graph of iii number equation- 

The graph of iv number equation-

From iii and iv number equation-

We get- P∞ IQ_________(iii)

              P∞ 1÷C_________(iv)

So, P∞ IQ×1÷C

Or, P∞ IQ÷C

So, P= HIQ÷C

From ii number equation-  P= IQ÷2C

So, H=½

The equation- P= IQ÷2C

Result:  

At last-

The value of capacitor’s power is proportional to the value of capacitor’s charge and electric conduction of circuit and disproportional to the value of capacitor’s capacitance. 

Conditions Of This Law:  

There are some conditions of this law. Here’s that-

i) This law is only for capacitor. 

ii) The position of capacitor should be in a circuit 

Conclusion:  

If we know the value of capacitor’s charge, capacitance and electric conduction of circuit we can determine the value of capacitor’s power.