Question

Compare and contrast the resistors and capacitors, separately combined, in a series and parallel settings.

Or

Describe house wiring and specify how parallel or series connections of bulbs and resistors affect the functions.

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Answer 1

ANS 1>

RESISTORS:

FIRST, the resistors in series and parallel.

In the first case we consider two resistors that are connected in series, as shown in the above figure,

Here it is clear that the same current flows throw both the resistors. this is always the case in case of series resistors.

Now Let us suppose That the voltage across nodes A and B is . The drop is sum of the voltage drops and across AND respectively.

According to the statement of Ohm's law, we can find out the equivalent resistance between nodes A and B is The ratio of the summation of the voltage drops across the two resistors and the The total current I flowing through them

Therefore,

Thus the equivalent resistance of resistors connected in series is the summation of their resistances.

now we will look at parallel resistances

From the above figure, we can notice that the Total Current I is getting divided into the two branches of the circuit containing two resistances, so the resistors in parallel have different values of current.

But the voltage drop V across the two resistors in the same in case of parallel resistors.

According to Ohm's Law we can find out the equivalent resistance of the circuit which is the ratio of the voltage to the summation of the different current values in the resistors,

Thus,

Thus we can say that the equivalent resistance of resistors connected in parallel is the summation of the reciprocals of their individual resistances.

CAPACITORS:

First we consider the case of series capacitors,

From, the above figure we see two capacitors in series with each other, and in this case the current I flowing through them is the same,

I =I₁ = I₂

Therefore we can say that, each capacitor connected in series, will store the same amount of electrical charge, Q, on its plates, regardless of their value of capacitance.This happens because the charge stored by the plate of one capacitor must have come from the plate of another capacitor that is connected in series with it.

Q_T = Q₁ = Q₂

In the above series circuit the voltage drop across each capacitor will be different depending upon the value of their capacitances,

V_T = (1)

and we know Q = C * V. Therefore,

V_C1 = Q₁/C₁ , V_C2 = Q₂/C₂

Then substituting in equation (1),

we get

So we get that , the equivalent value of capacitance in series is the summation of the reciprocal of individual capacitance values.

Now we will consider the case of capacitors  in parallel

From the above figure we see that the the capacitors connected in parallel, have different value of current flowing through them, and the The charge of each capacitor connected in parallel is dependent on the value of each capacitor as the voltage drop across each capacitor will be same,

Then the total value of capacitance for two capacitors connected in parallel is

There we can conclude that, the total capacitance of all the capacitors connected in parallel is the summation of the value of their individual capacitance.

Have a nice day