# Topic: Alternating Current (Test 1)

Topic: Alternating Current
Q.1
In a series LCR circuit supplied with AC
A. current in L and R is same but different in C
B. current in R and C is same but different in L
C. current in L and C is same but different in R
D. current in L, C and R is the same
Explaination / Solution:

In series circuits, the current always remains same while potential is different across different circuit components

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Q.2
If  , , and V represent the voltage across the inductor, resistor, capacitor and the source, respectively, on the phasor diagram
A.  and  are directed opposite to each other and  leads  by 90
B.  and  are directed opposite to each other and  leads  by 90
C.  and are at 90${}^{\circ }$ to each other and  leads  by 90
D.  and  are directed opposite to each other and  leads  by 90
Explaination / Solution:

In Series LCR Circuit, current is same across all elements. Since for a resistor both current and voltage are in same phase, Vis along the same direction as current in the phasor diagram.

In capacitor voltage lags current by 900 so it is at right angle with VR and in an inductor voltage leads current by 900 so it is at right angle with VR and directly opposite to Vc

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Q.3

If Vm and Im are peak voltage and current, Impedance Z in an AC circuit is

A. vmim
B. 2vmim
C. vm2im
D. vmim
Explaination / Solution:

Impedance refers to the overall obstruction offered by a circuit containing different components to the passage of current. Also Z has unit same as resistance.

So, drawing an analogy with the ohm's law, we get the above relation

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Q.4
The correct equation for a series LCR circuit excited by AC is
A. Ld2qdt2+Rdqdt+qC=vmsinωt
B. Ld2qdt2+Rdqdt+qC=0
C. Ld2qdt2+2Rdqdt+qC=0
D. Ld2qdt2+Rdqdt+2qC=vmsinωt
Explaination / Solution:

The LHS of equation contains expression for current through inductor, resistor and capacitor respectively. Each expression on LHS is a result of basic mathematical derivation. On the rhs we have the overall current in the circuit

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Q.5
The current in a series LCR circuit excited by AC of frequency ω is in general
A. Imsinωt
B. Imsin( + 90 )
C. 2Imsin()
D. Imsin (ωt+ϕ)
Explaination / Solution:

The above expression is for instantaneous value of current in an AC Circuit and since in an LCR circuit current is same across the circuit, the above expression holds valid for the entire LCR series circuit.

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Q.6
For a series LCR circuit the input impedance at resonance
A. equals the resistance ωL
B. equals the resistance R+jωL
C. equals the resistance R
D. equals the resistance 1/ωC
Explaination / Solution:

Impedance in series LCR circuit

at resonance

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Q.7
At resonance the current in an LCR circuit
A. is minimum
B. is zero
C. is local minimum
D. is maximum
Explaination / Solution:

in LCR series circuit current

at resonance

hence current will be maximum.

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Q.8
The sharpness of resonance is given by
A.  C
B. /R
C.  /C
D. /R
Explaination / Solution:

Sharpness of resonance is quantitatively described by a dimensionless number known as Q-factor or quality factor which is numerically equal to ratio of resonant frequency to bandwidth.

therefore

Q-factor = resonant frequency / bandwidth

sharpness of resonance =

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Q.9
For a parallel ideal LC circuit at resonance the input impedance across L or C is______
A. zero

LCLC
B. Equal to resistance
C. equal to XL
D. infinite
Explaination / Solution:

in parallel LC circuit, Impedance

at resonance

hence impedance will be infinite.

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Q.10
Transformer uses the follwing principle of
A. least action
B. charge conservation
C. Induction
D. conduction