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ycow [4]
3 years ago
14

Three conducting plates, each of area A, are connected as shown.

Physics
1 answer:
Shkiper50 [21]3 years ago
7 0
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)
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A wire of resistance R is cut into ten equal parts which are then connected in parallel. The equivalent resistance of the combin
Greeley [361]

Answer:

<em>The equivalent resistance of the combination is R/100</em>

Explanation:

<u>Electric Resistance</u>

The electric resistance of a wire is directly proportional to its length. If a wire of resistance R is cut into 10 equal parts, then each part has a resistance of R/10.

Parallel connection of resistances: If R1, R2, R3,...., Rn are connected in parallel, the equivalent resistance is calculated as follows:

\displaystyle \frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}

If we have 10 wires of resistance R/10 each and connect them in parallel, the equivalent resistance is:

\displaystyle \frac{1}{R_e}=\frac{1}{R/10}+\frac{1}{R/10}+\frac{1}{R/10}...+\frac{1}{R/10}

This sum is repeated 10 times. Operating each term:

\displaystyle \frac{1}{R_e}=\frac{10}{R}+\frac{10}{R}+\frac{10}{R}+...+\frac{10}{R}

All the terms have the same denominator, thus:

\displaystyle \frac{1}{R_e}=10\frac{10}{R}=\frac{100}{R}

Taking the reciprocals:

R_e=R/100

The equivalent resistance of the combination is R/100

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Answer:

The velocity of the boat with respect to the ground is 3 km/h

Explanation:

The speed of an object is different depending on the reference system you use. This is called relative speed.

A boat travels upstream, this means that it moves in the opposite direction to the river current.

A boat travels upstream, this means that it moves in the opposite direction to the river current. Then, if the boat moves in the positive direction of the x axis at 10 km / h with respect to the water of a river, the water flows in the negative direction of the x axis at 7 km / h with respect to the ground.

This causes the speed of the boat relative to the ground to be calculated as follows:  

<em>VbG = Vbw - VwG </em>

where VbG is the speed of the boat relative to the ground, Vbw is the speed of the boat relative to the water of the river and VwG is the speed of the water relative to the ground.

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<u><em>VbG= 3 km/h </em></u>

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