The driving point admittance of the network shown below is
∴
Figure shown below represents a d.c. 10 V voltage source as well as a 10 V a.c. 50 Hz voltage source while Z_{1} and Z_{2} are two unknown impedances. When Z_{1} is connected across 10V d.c. source, it draws a current of 10 A while it draws a current of 8 A if connected across 10V a.c. source.
Now, when Z_{2} is connected across 10 V d.c. source, it does not draw any current while it draws a current of 5 A if connected across 10 V a.c. source.
Q. What are the elements in Z_{1} and Z_{2}?
When Z_{1} is connected across d.c. source, it draws 10 A current.
Again, when Z_{1} is connected across a.c. source, it draws 8 A.
Thus,
Thus, Z_{1} = (1 + j0.75) Ω
Now, when Z_{2} is connected across 10 V d.c. source, it doesn’t draw any current. Hence, Z_{2} must be a capacitor which wilt act as open circuit for d.c. source.
Also, Z_{2} draws 5 A when connected to 10 V a.c. source.
or,
Thus, Z_{2} = j2 Ω
The current through the capacitor in the given circuit is
Since two voltage sources are present, we apply. Superposition theorem to find current through the capacitor i.e. current through j5 Ω, reactance.
Here,
and
So,
A parallel RLC circuit is said to be underdamped when
The characteristic equation of a parallel RLC circuit is
Also,
Thus,
and
for underdamped circuit, ξ < 1
Assertion (A): A coil, when connected across 230 V dc supply, will draw more current in comparison to that when connected across 230 V ac supply.
Reason (R): The inductance of the coil opposes the flow of alternating current (not that of direct current).
A two terminal black box contains one of the RLC elements. When the black box is connected to a 220 V ac supply, the current through the source is I. When a capacitance of 0.1 F is inserted in series between the source and the box, the current through the source is 2I. The element is
As current is increased therefore, new impedance should reduce. If the unknown element will be inductive, the new impedance will be (X_{L} X_{C}) Ω, so that the new value of current will increase.
A system function has a pole at s = 0 and zero at s = 1. The constant multiplier is unity. For an excitation cost, the steady state response is given by
Thus,
For the a.c. circuit given below, what is the value of I?
So,
Consider the following polezero diagram of a system,
What will be the magnitude of the voltage phasor for i(t) = sint?
From the polezero plot,
(Since sint = i(t); ω = 1 rad/s)
so,
A coil takes a current of 1∠60° A (lag) from a 100 V, 50 Hz supply. The resistance of the coil is
Also,
or, cos 60° = R/100
or, R = 100 cos 60°
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