Question

(1)Answer the following question: In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?

$2)$Answer the following question: A capacitor is used in the primary circuit of an induction coil. Why?

$3)$ Answer the following question:
An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across $C$ and the ac signal across$L.$

$4)$ Answer the following question: A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp’s brightness. Predict the corresponding observations if the connection is to an ac line.

$5)$Answer the following question: Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?

Answer 1

$1)$Yes, the statement is not true for rms voltage.
It is true that in any ac circuit, the applied
voltage is equal to the average sum of
the instantaneous voltages across the
series elements of the circuit.

However, this is not true for rms voltage
because voltages across different
elements may not be in phase

Final Answer: Yes. The same is not true for rms voltage

$2)$ A capacitor is used in the primary circuit of an induction coil.
This is because when the circuit breaks down, high voltage flows through the circuit.
If capacitor will be present, that extra voltage will be used up in charging the capacitor to avoid sparks.

Final Answer: If high induced voltage arises, it is utilized to charge the capacitor to avoid sparks.

$3)$
As we know,
$X_L=wL$

$X_c=\frac{1}{wC}$

For $DC$ supply, $w=0$

Then $X_L=0$ and $X_c=\infty$

The dc signal will appear across capacitor
$C$ because for dc signals, the impedance
of an inductor $\left(L\right)$ is negligible while the
impedance of a capacitor $\left(C\right)$ is very high (almost infinite). Hence, a dc signal appears across $C.$

For an ac signal of high frequency, the
impedance of $L$ is high and that of $C$ is very low. Hence, an ac signal of high frequency appears across $L$.

Final Answer: The dc signal will appear across $C$ and the ac signal across $L.$

$4)$For a steady-state $DC,$ choke (Inductor) has no impedance. Therefore, lamp shines brightly and there is no effect of inserting iron core in the choke.
On an $AC$ line, choke offers impedance. So, the bulb lights dimly.
When an iron core is inserted in the choke, its impedance to$AC$ increases further. Therefore, brightness of the bulb decreases.

Final Answer: Brightness of the bulb decreases.

$5)$A choke coil is needed in the use of fluorescent tubes to reduce ac without loss of power. If we use an ordinary resistor, ac will reduce, but loss of power due to heating will be there.
Power dissipated/cycle $=E_{rms}{I}_{rms}\cos \varphi$
In a resistor,$\varphi =0^{\circ }$
$\therefore$ Power dissipated/cycle
$=E_{rms}{I}_{rms}\cos 0^{\circ }$
$P_{Max}=E_{rms}{I}_{rms}$
Maximum power dissipation in resistor.
In a choke (inductor) coil, $\varphi ={90}^{\circ }$
$\therefore$ Power dissipated/cycle =
$E_{rms}{I}_{rms}\cos {90}^{\circ }$
$P_{Min}=0$

In a choke (inductor) coil,$\varphi ={90}^{\circ }$
$\therefore$ Power dissipated/cycle
$=E_{rms}{I}_{rms}\cos {90}^{\circ }$

$P_{Min}=0$
Minimum power dissipation in choke(inductor)

A choke coil reduces the voltage across the tube without wasting power, as average power consumed in inductive circuit is zero.

A resistor would waste power as heat, which will lead to loss of energy.

Final Answer: A resistor would waste power as heat.