The electric field between the plates of a paper-separated (K = 3.75) capacitor is 9.21 104 V/m. The plates are 2.05 mm apart and the charge on each plate is 0.775 µC. Determine the capacitance of this capacitor.
E= 8.18•10⁴ V/m
d=2.2 mm
q=0.775 μ C
ε (paper)= 2.3
(a) C=q/U
E=U/d
C=q/Ed = ...
(b)
ε₀=8.85•10⁻¹² F/m
C= ε₀εA/d =>
A=Cd/ε₀ε=...
Well, isn't that "capaci-fun"! To determine the capacitance of this capacitor, we can use the formula C = Q / V, where C is the capacitance, Q is the charge on each plate, and V is the electric field between the plates.
Plugging in the values we have, the charge (Q) is 0.775 µC and the electric field (V) is 9.21 x 10^4 V/m.
So, the capacitance (C) is given by C = (0.775 µC) / (9.21 x 10^4 V/m).
But hold on a second! We have to convert the charge from microCoulombs to Coulombs first. Since there are 10^-6 C in 1 µC, the charge becomes 0.775 x 10^-6 C.
Substituting this value into our equation, we get C = (0.775 x 10^-6 C) / (9.21 x 10^4 V/m).
Simplifying a bit, we have C = 8.40 x 10^-12 F.
So, the clown-approved answer is that the capacitance of this capacitor is 8.40 picofarads (pF). Isn't that positively electrifying?
To determine the capacitance of the capacitor, you can use the formula:
C = Q / V
where C is the capacitance, Q is the charge on each plate, and V is the electric field.
In this case, the charge on each plate is given as 0.775 µC, which is equivalent to 0.775 × 10^(-6) C. The electric field is given as 9.21 × 10^4 V/m.
Plugging these values into the formula, we have:
C = (0.775 × 10^(-6) C) / (9.21 × 10^4 V/m)
Now, calculating the capacitance:
C = 0.775 × 10^(-6) C / 9.21 × 10^4 V/m
C = 0.084 µF
Therefore, the capacitance of this capacitor is 0.084 µF.
To determine the capacitance of the capacitor, we can use the formula:
C = Q / V
Where:
- C is the capacitance
- Q is the charge on each plate
- V is the voltage between the plates
Given:
Q = 0.775 µC (microCoulombs)
V = 9.21 × 10^4 V/m (Volts per meter)
We need to convert the charge from microCoulombs to Coulombs by dividing it by 10^6:
Q = 0.775 × 10^(-6) C
Now we can substitute these values into the formula to calculate the capacitance:
C = (0.775 × 10^(-6) C) / (9.21 × 10^4 V/m)
Simplifying:
C = 0.775 × 10^(-6) / 9.21 × 10^4
C = 8.41 × 10^(-11) F
Therefore, the capacitance of the capacitor is 8.41 × 10^(-11) Farads.