Capacitor Lab (5/5) (Capacitance)
We define the dependence on how much charge a capacitor can hold at a given potential difference as capacitance.
Capacitance is the ratio of charge/potential difference:
C=Q/ΔV
We measure this quantity in a unit called Farads, which is a very large unit. Most capacitors we use are masured in microfarads, nanofarads, or picofarads.
Note that we are using Q instead of q for charge. This is to distinguish between small charges and the total charge on the device.
Since Q=CΔV, we can explain the patterns we saw in lab. For a given potential, it's the capacitance that's changing as we change the capacitor geometry. We saw bigger plates caused more Q. That means more C. Plates that were further apart caused less Q. That means less C. So we see that C=kA/d. The constant in this case is a fundamental constant that we abbreviate as ε˳ which we call the permittivity. It's a constant like G, or π. It will always be given to you.
We can also use the definition of capacitance to understand the dependence of energy stored on electric potential. Since U=QV, we can plug Q=CV in to get a dependence of energy on potential and capacitance. As we charge a capacitor, it goes from zero potential difference to a final potential difference. The average potential for the capacitor as it charges is (0+V)/2. So we can plug CV in to Q, and (½V) in for V.
Capacitor Lab (5/5) (Capacitance)
We define the dependence on how much charge a capacitor can hold at a given potential difference as capacitance.
Capacitance is the ratio of charge/potential difference:
C=Q/ΔV
We measure this quantity in a unit called Farads, which is a very large unit. Most capacitors we use are masured in microfarads, nanofarads, or picofarads.
Note that we are using Q instead of q for charge. This is to distinguish between small charges and the total charge on the device.
Since Q=CΔV, we can explain the patterns we saw in lab. For a given potential, it's the capacitance that's changing as we change the capacitor geometry. We saw bigger plates caused more Q. That means more C. Plates that were further apart caused less Q. That means less C. So we see that C=kA/d. The constant in this case is a fundamental constant that we abbreviate as ε˳ which we call the permittivity. It's a constant like G, or π. It will always be given to you.
We can also use the definition of capacitance to understand the dependence of energy stored on electric potential. Since U=QV, we can plug Q=CV in to get a dependence of energy on potential and capacitance. As we charge a capacitor, it goes from zero potential difference to a final potential difference. The average potential for the capacitor as it charges is (0+V)/2. So we can plug CV in to Q, and (½V) in for V.