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JEE Mains | PYQ

In a meter bridge experiment the balance point is obtained if the gaps are closed by \( 2\Omega \) and \( 3\Omega \). A shunt of \( X\Omega \) is added to \( 3\Omega \) resistor to shift the balancing point by \( 22.5 \, \text{cm} \). The value of \( X \) is ____.

The equivalent resistance between \( A \) and \( B \) is ___________.

A uniform metallic wire carries a current \( 2 \, \text{A} \), when \( 3.4 \, \text{V} \) battery is connected across it. The mass of uniform metallic wire is \( 8.92 \times 10^{-3} \, \text{kg} \), density is \( 8.92 \times 10^{3} \, \text{kg}/\text{m}^{3} \) and resistivity is \( 1.7 \times 10^{-8} \, \Omega\text{-m} \). The length of wire is:

A potential \( V_{0} \) is applied across a uniform wire of resistance \( R \). The power dissipation is \( P_{1} \). The wire is then cut into two equal halves and a potential of \( V_{0} \) is applied across the length of each half. The total power dissipation across two wires is \( P_{2} \). The ratio \( P_{2} : P_{1} \) is \( \sqrt{x} : 1 \). The value of \( x \) is ________.

Two identical cells each of emf \( 1.5 \, \text{V} \) are connected in series across a \( 10 \, \Omega \) resistance. An ideal voltmeter connected across \( 10 \, \Omega \) resistance reads \( 1.5 \, \text{V} \). The internal resistance of each cell is _______ \( \Omega \).

As shown in the figure, a network of resistors is connected to a battery of \( 24 \, \text{V} \) with an internal resistance of \( 3 \, \Omega \). The currents through the resistors \( R_4 \) & \( R_5 \) are \( I_4 \) & \( I_5 \) respectively. The values of \( I_4 \) & \( I_5 \) are :

In the circuit diagram shown in figure given below, the current flowing through resistance \( 3\Omega \) is \( \dfrac{x}{3} \, \text{A} \).
The value of \( x \) is _________.

If the potential difference between \( B \) and \( D \) is zero, the value of \( x \) is \( \frac{1}{n} \, \Omega \). The value of \( n \) is _______.

Given below are two statements:
Statement I: The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.
Statement II: The resistivity of the material is independent of temperature.
In the light of the above statements, choose the correct answer from the options given below:

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf \( 1.5\,\text{V} \) is found to be \( 60\,\text{cm} \). If this cell is replaced by another cell of emf \( E \), the length of null point increases by \( 40\,\text{cm} \). The value of \( E \) is \( \frac{x}{10}\,\text{V} \). The value of \( x \) is ________.

When two resistances \( R_1 \) and \( R_2 \) connected in series and introduction into the left gap of a meter bridge and a resistance of \( 10 \, \Omega \) is introduced into the right gap, a null point is found at \( 60 \, \text{cm} \) from left side. When \( R_1 \) and \( R_2 \) are connected in parallel and introduced into the left gap, a resistance of \( 3 \, \Omega \) is introduced into the right-gap to get null point at \( 40 \, \text{cm} \) from left end. The product of \( R_1 R_2 \) is _____ \( \Omega^2 \).

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by \( 50\% \). The percentage change in voltage sensitivity of the galvanometer will be:

A current of \( 2 \, \text{A} \) flows through a wire of cross-sectional area \( 25.0 \, \text{mm}^{2} \). The number of free electrons in a cube meter are \( 2.0 \times 10^{28} \). The drift velocity of the electrons is ________ \( \times 10^{-6} \, \text{m}\,\text{s}^{-1} \).
(Given, charge on electron \( = 1.6 \times 10^{-19} \, \text{C} \))

The \( H \) amount of thermal energy is developed by a resistor in \( 10 \, \text{s} \) when a current of \( 4 \, \text{A} \) is passed through it. If the current is increased to \( 16 \, \text{A} \), the thermal energy developed by the resistor in \( 10 \, \text{s} \) will be:

A rectangular parallelepiped is measured as \( 1 \, \text{cm} \times 1 \, \text{cm} \times 100 \, \text{cm} \). If its specific resistance is \( 3 \times 10^{-7} \, \Omega \, \text{m} \), then the resistance between its two opposite rectangular faces will be ______ \( \times 10^{-7} \, \Omega \).

Two identical cells, when connected either in parallel or in series gives same current in an external resistance \( 5 \, \Omega \). The internal resistance of each cell will be ____ \( \Omega \).

The current flowing through \( R_{2} \) is:

In the given circuit, the equivalent resistance between the terminal \( A \) and \( B \) is ____________ \( \Omega \).

In the given circuit, the value of \( \left|\frac{I_{1}+I_{3}}{I_{2}}\right| \) is _______.

The equivalent resistance between \( A \) and \( B \) as shown in figure is:

The current sensitivity of moving coil galvanometer is increased by \( 25\% \). This increase is achieved only by changing in the number of terms of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:

A wire of resistance \( 160 \, \Omega \) is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: For measuring the potential difference across a resistance of \( 600 \, \Omega \), the voltmeter with resistance \( 1000 \, \Omega \) will be preferred over voltmeter with resistance \( 4000 \, \Omega \).
Reason R: Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.
In the light of the above statements, choose the most appropriate answer from the options given below:

For the given circuit, in the steady state, \( |V_{B}-V_{D}| = \) ______ V.

\( 10 \) resistors each of resistance \( 10 \, \Omega \) can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be _______.

The equivalent resistance of the circuit shown below between points a and b is:

The resistance of a wire is \( 5\,\Omega \). It’s new resistance in ohm if stretched to \( 5 \) times of it’s original length will be:

The drift velocity of electrons for conductor connected in an electrical circuit is \( V_d \). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be:

For designing a voltmeter of range \( 50 \, \text{V} \) and an ammeter of range \( 10 \, \text{mA} \) using a galvanometer which has a coil of resistance \( 54 \, \Omega \) showing a full scale deflection for \( 1 \, \text{mA} \) as in figure.

(A) for voltmeter \( R \approx 50 \, \text{k}\Omega \)         (B) for ammeter \( r \approx 0.2 \, \Omega \)
(C) for ammeter \( r = 6 \, \Omega \)                (D) for voltmeter \( R \approx 5 \, \text{k}\Omega \)
(E) for voltmeter \( R \approx 500 \, \Omega \)
Choose the correct answer from the options given below:

Two cells are connected between points \( A \) and \( B \) as shown. Cell \( 1 \) has emf of \( 12 \, \text{V} \) and internal resistance of \( 3 \, \Omega \). Cell \( 2 \) has emf of \( 6 \, \text{V} \) and internal resistance of \( 6 \, \Omega \). An external resistor \( R \) of \( 4 \, \Omega \) is connected across \( A \) and \( B \). The current flowing through \( R \) will be ______ \( \text{A} \).

Equivalent resistance between the adjacent corners of a regular \( n \)-sided polygon of uniform wire of resistance \( R \) would be:

In the circuit shown, the energy stored in the capacitor is \( n \, \mu \text{J} \). The value of \( n \) is __________.

A hollow cylindrical conductor has length of \( 3.14 \, \mathrm{m} \), while its inner and outer diameters are \( 4 \, \mathrm{mm} \) and \( 8 \, \mathrm{mm} \) respectively. The resistance of the conductor is \( n \times 10^{-3} \, \Omega \). If the resistivity of the material is \( 2.4 \times 10^{-8} \, \Omega \, \mathrm{m} \). The value of \( n \) is ______.

Given below are two statements:
Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio
In the light of the above statements, choose the correct answer from the options given below:

In the following circuit, the magnitude of current \( I_{1} \) is _______ \( \text{A} \).

When a resistance of \( 5 \, \Omega \) is shunted with a moving coil galvanometer, it shows as full scale deflection for a current of \( 250 \, \text{mA} \), however when \( 1050 \, \Omega \) resistance is connected with it in series, it gives full scale deflection for \( 25 \, \text{volt} \). The resistance of galvanometer is ______ \( \Omega \).

Different combination of \( 3 \) resistors of equal resistance \( R \) are shown in the figures. The increasing order for power dissipation is:

The number density of free electrons in copper is nearly \( 8 \times 10^{28} \, \text{m}^{-3} \). A copper wire has its area of cross section \( = 2 \times 10^{-6} \, \text{m}^2 \) and is carrying a current of \( 3.2 \, \text{A} \). A drift speed of the electrons is ______ \( \times 10^{-6} \, \text{ms}^{-1} \).

As shown in the figure, the voltmeter reads \( 2 \, \text{V} \) across \( 5 \, \Omega \) resistor. The resistance of the voltmeter is _________ \( \Omega \).
 

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

A network of four resistances is connected to \( 9 \, \text{V} \) battery, as shown in figure. The magnitude of voltage difference between the points \( A \) and \( B \) is __________ \( \text{V} \).

In a metallic conductor, under the effect of applied electric field the free electrons of the conductor.

Figure shows a part of an electric circuit. The potentials at points \( a \), \( b \) and \( c \) are \( 30 \, \text{V} \), \( 12 \, \text{V} \) and \( 2 \, \text{V} \) respectively. The current through the \( 20 \, \Omega \) resistor will be: