Physics

CBSE Class 12

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1.
_{C} = X_{L} is inserted in series in the circuit. Justify your answer in each case.

An inductor L of inductance X_{L }is connected in series with a bulb B and an ac source.

i) Net resistance in the circuit is given by,

Inductance is given by,

As number of turns decreases, L decreases.

Inductance is given by,

Therefore, will also decrease thereby, reducing the net resistance in the circuit. Thus, current increases and brightness of the bulb is increased.

ii) When a soft iron rod is inserted in the circuit, L increases. Therefore, inductive reactance also increases. Net resistance increases and flow of current in the circuit decreases. Thus, the brightness of the bulb will decrease.

iii) When a capacitor of reactance X_{L} = X_{C} is connected in series with the circuit net resistance becomes,

; where R is the resistance of the bulb.

Here, we will have Z= R which is the condition of resonance.

At resonance, maximum current will flow through the circuit. Therefore, the brightness of the bulb will increase.

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2.
Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone bridge.

A Wheatstone bridge arrangement is shown as below:

Using Kirchoff’s second law to the loop ABDA, we get

Applying Kirchoff’s law to loop BCDB, we get

When the bridge is balanced,

Then, the equations can be written as,

... (1)

... (2)

On dividing equation (1) by (2), we get

, which is the balanced condition of a Wheatstone bridge.

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3.
_{1} in series with the coil. If a resistance R_{2} is connected in series with it, then it can measure upto V/2 volts. Find the resistance, in terms of R_{1} and R_{2}, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the galvanometer in terms of R_{1} and R_{2}.

State the principle of working of a galvanometer.

A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance RPrinciple:

When a current carrying loop or coil is placed in the uniform magnetic field, moving coil galvanometer experiences a torque.

A high resistance is connected in series with the galvanometer to convert it into a voltmeter.

The value of resistance is given by,

where,

V is the potential difference across the terminals of the voltmeter.

is current through galvanometer and

G is the resistance of the galvanometer.

When resistance R_{1} is connected in series with the galvanometer,

When resistance R_{2} is connected in series with the galvanometer,

... (2)

From equations (1) and (2), we get

Resistance R_{3} required to convert galvanometer into voltmeter of range 0 to 2V is given by,

Therefore, R_{1} - 2R_{2 }is the galvanometer resistance in terms of R_{1} and R_{2}

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4.

Name the parts of the electromagnetic spectrum which is

(a) suitable for radar systems used in aircraft navigation.

(b) used to treat muscular strain.

(c) used as a diagnostic tool in medicine.

Write in brief, how these waves can be produced.a) Microwaves are suitable for Radar system used in air navigation. They are produced by special vacuum tubes namely klystron valve or magnetron valve.

b) Infrared waves are used to treat muscular strain. These ways are produced by the vibration of atoms and molecules.

c) X-rays are used as diagnostic tool in medicine. X-rays are produced when high energy electrons are suddenly stopped on metal of high atomic number and by the radio-active decay of nucleus.

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5.
A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens ?

Here, a concave lens is placed in a medium of refractive index greater than the refractive index of the material of the lens.

So, the given lens will behave as a diverging lens.

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The resistance offered by the capacitor when connected to an electrical circuit is known as capacitive reactance.

It is given by,

where,

is the angular frequency of the source, and

C, is the capacitance of the capacitor.

SI Unit is ohm.

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7.
What is the electric flux through a cube of side 1 cm which encloses an electric dipole?

Given, cube encloses an electric dipole.

So, the total charge enclosed by the cube is zero.

That is, Q= 0.

Now, using the formula for electric flux as per the Gauss’s law of electrostatics, we have

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8.

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.

It is found that when R = 4 , the current is 1 A and when R is increased to 9 , the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.Plot for V vs. R

Plot for V vs. I

Current in the circuit is given by,

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9.

Graph showing the variation of current versus voltage for a material GaAs is shown in the figure. Identify the region of

i) negative resistance

ii) where Ohm’s law is obeyed.i) The region of negative resistance is DE because, the slope is negative for this part of curve.

ii) BC is the part of the curve where Ohm’s law is obeyed because here, current is varying linearly with with the voltage. This gives us direct proportionality between current and voltage.

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10.

Two capacitors of unknown capacitances C_{1} and C_{2} are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C_{1} and C_{2}. Also, calculate the charge on each capacitor in parallel combination.

When the capacitors are connected in parallel,

Equivalent resistance,

Energy stored in capacitors, E_{P } =

When the capacitors are connected in series,

Putting this in equation (2), we get

C_{2 = }50 – 11.2 = 38.2 μF

The charge on capacitor is given by, Q = CV

Charge on capacitor 1, C_{1} =

Charge on capacitor 2, C_{2 }=

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