Physics, 27.03.2020 20:21 gwendallinesikes

The resultant capacitance of four capacitors connected in series is the smallest individual capacitance
a)less than b)greater than c)equals to d) four times

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Answer from: mollykay2001p3qo0j

a)less than

Explanation:

The resultant capacitance of N capacitors connected in series is given by

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+....+\frac{1}{C_N}$

In this problem, since we have 4 capacitances in series, the resultant capacitance is

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\frac{1}{C_4}$

Each of the single term on the right-side of the equation is a positive term: this means that the term $\frac{1}{C}$ will be larger than the individual terms $\frac{1}{C_i}$ .

Therefore, this means that the reciprocal, C, will be smaller than each of the individual capacitances C_i .

In particular, if the 4 capacitances are identical,

C_1=C_2=C_3=C_4=C_0

So the resultant capacitance will be:

$\frac{1}{C}=4\frac{1}{C_0}\\\rightarrow C=\frac{C_0}{4}$

So the correct answer is

a) less than

Answer from: Quest

Less force and energy was applied

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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