You have effectively got two capacitors in parallel. The effective capacitance is just the sum of the two.
Cequiv = ε₀A/d₁ + ε₀A/d₂ Take these over a common denominator (d₁d₂)
Cequiv = ε₀d₂A + ε₀d₁A / (d₁d₂) Cequiv = ε₀A( (d₁ + d₂) / (d₁d₂) )
B) It's tempting to just wave your arms and say that when d₁ or d₂ tends to zero C -> ∞, so the minimum will occur in the middle, where d₁ = d₂
But I suppose we ought to kick that idea around a bit.
(d₁ + d₂) is effectively a constant. It's the distance between the two outer plates. Call it D.
C = ε₀AD / d₁d₂ We can also say: d₂ = D - d₁ C = ε₀AD / d₁(D - d₁) C = ε₀AD / d₁D - d₁²
Differentiate with respect to d₁
dC/dd₁ = -ε₀AD(D - 2d₁) / (d₁D - d₁²)² {d2C/dd₁² is positive so it will give us a minimum} For max or min equate to zero.
-ε₀AD(D - 2d₁) / (d₁D - d₁²)² = 0 -ε₀AD(D - 2d₁) = 0 ε₀, A, and D are all non-zero, so (D - 2d₁) = 0 d₁ = ½D
In other words when the middle plate is halfway between the two outer plates, (quelle surprise) so that
d₁ = d₂ = ½D so
Cmin = ε₀AD / (½D)² Cmin = 4ε₀A / D Cmin = 4ε₀A / (d₁ + d₂)
It’s A.Longitudinal. Tell me if I’m right
Answer:
Force, F = 44 N
Explanation:
Given that,
Initial speed of the football, u = 0
Final speed, v = 15 m/s
The time of contact of the ball, t = 0.15 s
The mass of football, m = 0.44 kg
We need to find the average force exerted on the ball. It is given by the formula as :
So, the average force exerted on the ball is 44 N. Hence, this is the required solution.
Explanation:
Particles in solids are always vibrating (moving back and forth) in place.
Answer:
1.11×10⁸ Electrons.
Explanation:
Applying,
Q = CV..................... Equation 1
Where Q = Total charge on the capacitor, C = Capacitance of the capacitor, V = Voltage of the battery.
Given: C = 1.97 pF = 1.97×10⁻¹² F, V = 9.0 V
Substitute this value into equation 1
Q = 1.97×9×10⁻¹²
Q = 1.773×10⁻¹¹ C.
If the charge on one electron = 1.602×10⁻¹⁹ C.
Therefore number of electron = 1.773×10⁻¹¹ /1.602×10⁻¹⁹
Number of electron = 1.11×10⁸
