A 2600-pF air gap capacitor is connected to a 9.0 V battery.If a piece of pyrex glass is placed between the plates,how much charge will then flow from the battery?
According to one website I found, "The dielectric constant of Pyrex is relatively low, in the range of 4.0 to 6.0" They may have provided you with a value already.
To determine how much charge will flow from the battery when a piece of pyrex glass is placed between the plates of a 2600-pF air gap capacitor connected to a 9.0 V battery, we need to calculate the effect of the pyrex glass on the capacitance of the system.
The capacitance (C) of a parallel plate capacitor is given by the formula:
C = (ε₀ * A) / d
where:
- C is the capacitance
- ε₀ is the permittivity of free space (8.85 x 10⁻¹² F/m)
- A is the area of the plates
- d is the separation distance between the plates
Given that the initial capacitance of the air gap capacitor is 2600 pF (picofarads) and the voltage of the battery is 9.0 V, we can assume the plates are already separated by air initially.
Now, when the pyrex glass is placed between the plates, it acts as a dielectric material, which changes the capacitance of the system. The relative permittivity (εᵣ) of pyrex glass is around 4.85. Therefore, the new capacitance (C') can be calculated as:
C' = εᵣ * C
Substituting the values, we have:
C' = 4.85 * 2600 pF
Now, we can calculate the charge (Q) flowing from the battery using the formula:
Q = C' * V
where:
- Q is the charge
- C' is the new capacitance
- V is the voltage of the battery
Substituting the values, we have:
Q = (4.85 * 2600 pF) * 9.0 V
To get the final answer, convert picofarads (pF) to farads (F) by dividing by 10⁻¹²:
Q = (4.85 * 2600 * 10⁻¹² F) * 9.0 V
Now, solve the equation to find the value of Q.
Calculate the new Capacitance, C', by multiplying the original C by the dielectric constant of Pyrex, k.
The added charge will be V*(C'-C)=
= (k-1)C V