Test: Capacitors & Inductors - 1
15 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Capacitors & Inductors - 1
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An Inductor works as a ________ circuit for DC supply.
Induced voltage across an inductor is zero if the current flowing through it is constant, i.e. Inductor works as a short circuit for DC supply.
A power factor of a circuit can be improved by placing which, among the following, in a circuit?
Power factor = Real power / Apparent power = kW/kVA
By adding a capacitor in a circuit, an additional kW load can be added to the system without altering the kVA.
Hence, the power factor is improved.
Which among the following equations is incorrect?
- Q is directly proportional to V.
- The constant of proportionality in this case is C, that is, the capacitance.
- Hence Q=CV. From the given relation we can derive all the equations except for Q = C/V.
What is the value of capacitance of a capacitor which has a voltage of 4V and has 16C of charge?
Q is directly proportional to V.
The constant of proportionality in this case is C, that is, the capacitance.
Hence Q = CV
From the relation,
C = Q/V = 16/4 = 4F
What is the total capacitance when two capacitors C1 and C2 are connected in series?
When capacitors are connected in series, the equivalent capacitance is:
1/Ctotal=1/C1 + 1/C2
therefore,
Ctotal = C1*C2 / (C1+C2)
A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a 100V 50Hz sinusoidal supply. Calculate the current in the circuit.
XL = 2*π*f*L = 10 ohm
Z2 = (R2+XL2)
Therefore the total impedance
Z = 12.2 ohm
V = IZ
therefore,
I= V/Z = 100/12.2 = 8.2A
The equivalent circuit of the capacitor shown below is:
Due to initial condition, at t = 0 capacitor will act as a constant voltage source (at t = 0, capacitor acts as short-circuit). Hence, option (d) is correct.
The strength of current in 1 Henry inductor changes at a rate of 1 A/sec. The magnitude of energy stored in the inductor after 3 sec is:
∴ Current in the inductor after 3 sec is:
1= 3 A
Hence, energy is stored after 3 sec:
The current and voltage profile of an element vs time has been shown in given figure. The element and its value are respectively:
- Since V is not proportional to R therefore, the element can’t be a resistor.
- At t = 5 ms, even if i ≠ 0, the element behaves as a short circuit therefore, the element can’t be a capacitor (since at t = 0 only capacitor behaves as short circuit).
- The current at t = 0 is zero and at t = 5 ms voltage across the element is zero therefore, the element must be an inductor (at t = 0, an inductor acts as open circuit and at t =∞ it behaves as short circuit).
- From the given voltage and current profile, we have:
Figure shown below exhibits the voltage-time profile of a source to charge a capacitor of 50 μF. The value of charging current in amperes is:
From given figure:
The equivalent capacitance across the given terminals A-B is:
- The equivalent combination of C2 and C3
- The equivalent combination of this 1 μF and C1 = 2μF is C1+ 1 μF = 3μF
- Hence, the equivalent capacitance between terminals A and B is
The charging time required to charge the equivalent capacitance between the given terminals a-b by a steady direct current of constant magnitude of 10 A is given by:
Equivalent capacitance between terminals a-b is:
An ac voltage of 220 V is applied to a pure inductance of 50 H. If the current is 5 A, the instantaneous value of voltage and current will be respectively given by:
Max. value of current:
Assuming voltage as the reference phasor:
The voltage and current through a circuit element is v= 100 sin (314 t + 45°) volts and i = 10 sin (314 t - 45 ° ) amps.
The type of circuit element and its value will be respectively:
The phase difference between v and i is:
Since v leads i therefore, the circuit element is an inductor.
The equivalent inductance for the inductive circuit shown below at terminal “ 1 - 2 ” is:
Converting the internal star connected inductance to an equivalent delta, the circuit reduces as shown below.
Hence, equivalent circuit becomes as shown below.
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