Answer.1. I_t = I_R − Ij_L

Explanation:-

Phase Relationships of Currents and Voltages for parallel RL circuit

Figure (a) shows all the currents in a basic parallel RL circuit. The total current I_t divides at the junction into the two branch currents, I_R and I_L. The applied voltage V_s appear across both the resistive and the inductive branches, so V_s, V_r, and V_L are all in phase and of the same magnitude.

The current through the resistor is in phase with the voltage. The current through the inductor lags the voltage and the resistor current by 90°. By Kirchhoff’s current law, the total current is the phasor sum of the two branch currents, as shown by the phasor diagram in Figure (b). The total current is expressed as

I_t = I_R − Ij_L

Answer.4. 54.5 mA − j80 mA

Explanation:-

From the given figure the resistor current, the inductor current, and the total current are

I_R = V_s/R = 12∠0°/220∠0° = 54.5∠0° mA

I_L = V_s/X_L = 12∠0°/150∠90° = 80∠−90° mA

I_t = I_R − Ij_L

I_t = 54.5 mA − j80 mA

Answer.2. Inductor

Explanation:-

In a purely inductive ac circuit, all of the energy delivered by the source is stored by the inductor in its magnetic field during a portion of the voltage cycle and then returned to the source during another portion of the cycle so that there is no net energy conversion to heat.

Answer.4. Greater than

Explanation:-

When the resistance in a series RL circuit is greater than the inductive reactance, more of the total energy delivered by the source is converted to heat by the resistance than is stored by the inductor. Likewise, when the reactance is greater than the resistance, more of the total energy is stored and returned than is converted to heat.

Answer.4. P = I² X_L

Explanation:-

The power dissipation in resistance is called the true power. The power in an inductor is reactive power and is expressed as

P = I² X_L

Answer.2. Less, More

Explanation:-

The power factor equals the cosine of θ (PF = Cosθ).

As the phase angle between the applied voltage and the total current increases, the power factor decreases, indicating an increasingly reactive circuit. A smaller power factor indicates less true power and more reactive power.

Answer.1. 0.448

Explanation:-

I_R = V_s/R = 12∠0°/220∠0° = 54.5∠0° mA

I_L = V_s/X_L = 12∠0°/150∠90° = 80∠−90° mA

I_t = I_R − Ij_L

I_t = 54.5 mA − j80 mA

The total impedance of the circuit is

Z = R + jX_L

Z = (1 + J2)kΩ

Converting to polar form

$\begin{array}{l} {\rm{Z = }}\sqrt {{R^2} + {X^2}_L} \angle {\tan ^{ – 1}}\left( {\dfrac{{{X_L}}}{R}} \right)\\ \\ {\rm{Z = }}\sqrt {{{(1)}^2} + {{(2)}^2}} \angle {\tan ^{ – 1}}\left( {\dfrac{2}{1}} \right) \end{array}$

Z = 2.24∠63.4°

The phase angle indicated in the expression for Z, is

θ = 63.4°

The power factor is, therefore,

PF = cosθ = cos(63.4°) = 0.448

Answer.3. Zero

Explanation:-

When the power factor is zero, all of the current to a load is 90° out of phase with the voltage (reactive).

Answer.3. Parallel

Explanation:-

If the load consists of a series connection of a resistor with resistance R and an inductor with inductance L adding a parallel capacitor with capacitance value C can increase the power factor to the desired value. The power factor of an inductive load can be increased by the addition of a capacitor in parallel, as shown in Figure. The capacitor compensates for the phase lag of the total current by creating a capacitive component of current that is 180° out of phase with the inductive component. This has a canceling effect and reduces the phase angle and the total current and increases the power factor, as illustrated in the figure.

Answer.1. Series

Explanation:-

The basic function of a low pass filter is to pass low frequencies with very little loss and to attenuate high frequencies. A familiar application of low pass filters is in the tone control of hi-fi amplifiers. The treble control varies the cut-off frequency of an LP filter and is used to attenuate the high-frequency noise.

Two circuits that behave as low pass filters are the series RL circuit and the series RC circuit.