`R`

`4.142. A coil and an inductance-free resistance R = 25 Q are`

connected in parallel to the ac mains. Find the heat power generated

in the coil provided a current I = 0.90 A is drawn from the mains.

The coil and the resistance R carry currents I, = 0.50 A and / 2 =

= 0.60 A respectively.

4.143. An alternating current of frequency co = 314 s- 1 is fed

to a circuit consisting of a capacitor of capacitance C = 73 p,F and

an active resistance R = 100 Q connected in parallel. Find the impe-

dance of the circuit.

4.144. Draw the approximate vector diagrams of currents in the

circuits shown in Fig. 4.35. The voltage applied across the points A

and B is assumed to be sinusoidal; the parameters of each circuit are

so chosen that the total current / 0 lags in phase behind the external

voltage by an angle cp.

(a)

(6) (0)

Fig. 4.35.

4.145. A capacitor with capacitance C = 1.0 p,F and a coil with

active resistance R = 0.10 Q and inductance L = 1.0 mH are con-

nected in parallel to a source of sinusoidal voltage V = 31 V. Find:

(a) the frequency co at which the resonance sets in;

(b) the effective value of the fed current in resonance, as well as

the corresponding currents flowing through the coil and through the

capacitor.

4.146. A capacitor with capacitance C and a coil with active resis-

tance R and inductance L are connected in parallel to a source of

sinusoidal voltage of frequency co. Find the phase difference between

the current fed to the circuit and the source voltage.

4.147. A circuit consists of a capacitor with capacitance C and

a coil with active resistance R and inductance L connected in paral-

lel. Find the impedance of the circuit at frequency co of alternating

voltage.

4.148. A ring of thin wire with active resistance R and inductance L

rotates with constant angular velocity co in the external uniform

magnetic field perpendicular to the rotation axis. In the process, the

flux of magnetic induction of external field across the ring varies with

time as 413 = 0 0 cos cot. Demonstrate that

(a) the inductive current in the ring varies with time as I =

= In, sin (cot — cp), where I m = col:13 0 11CM --F- co 2 L 2 with tan cp =

coL/R;

(b) the mean mechanical power developed by external forces to

maintain rotation is defined by the formula P = i120)^2 cD2Ri (R2 +

co 2L2).

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