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An electric bulb of \( 500 \, \text{watt} \) at \( 100 \, \text{volt} \) is used in a circuit having a \( 200 \, \text{V} \) supply. Calculate the resistance \( R \) to be connected in series with the bulb so that the power delivered by the bulb is \( 500 \, \text{W} \).

The value of current in the \( 6 \, \Omega \) resistance is:

Five identical cells each of internal resistance \( 1\,\Omega \) and emf \( 5\,\text{V} \) are connected in series and in parallel with an external resistance \( R \). For what value of \( R \), current in series and parallel combination will remain the same?

A current of \( 10 \, \text{A} \) exists in a wire of crossectional area of \( 5 \, \text{mm}^{2} \) with a drift velocity of \( 2 \times 10^{-3} \, \text{m s}^{-1} \). The number of free electrons in each cubic meter of the wire is ________.

In the given figure, there is a circuit of potentiometer of length \( AB = 10 \, \text{m} \). The resistance per unit length is \( 0.1 \, \Omega / \text{cm} \). Across \( AB \), a battery of emf \( E \) and internal resistance '\( r \)' is connected. The maximum value of emf measured by this potentiometer is:

A copper (Cu) rod of length \( 25 \, \mathrm{cm} \) and cross-sectional area \( 3 \, \mathrm{mm^2} \) is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.
(Take Resistivity of Copper \( = 1.7 \times 10^{-8} \, \Omega \,\mathrm{m} \) , Resistivity of Aluminium \( = 2.6 \times 10^{-8} \, \Omega \,\mathrm{m} \) )

The resistance of a conductor \( 15^\circ \text{C} \) is \( 16 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 20 \, \Omega \). What will be the temperature coefficient of resistance of the conductor?

Seawater at a frequency \( f = 9 \times 10^2\,Hz \), has permittivity \( \varepsilon = 80\,\varepsilon_0 \) and resistivity \( \rho = 0.25\,\Omega m \). Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source \( V(t) = V_0 \sin(2 \pi ft) \). Then the conduction current density becomes \( 10^x \) times the displacement current density after time \( t = \dfrac{1}{800}\,s \). The value of \( x \) is ________.
(Given: \( \dfrac{1}{4\pi \varepsilon_0} = 9 \times 10^9\, N m^2 C^{-2} \))

The equivalent resistance of series combination of two resistor is ‘\( s \)’. When they are connected in parallel, the equivalent resistance is ‘\( p \)’. If \( s = n p \), then the minimum value for \( n \) is ______. (Round off to the Nearest Integer)

Two wires of same length and thickness having specific resistances \( 6 \, \Omega \, \text{cm} \) and \( 3 \, \Omega \, \text{cm} \) respectively are connected in parallel. The effective resistivity is \( \rho \, \Omega \, \text{cm} \). The value of \( \rho \), to the nearest integer is:

A \( 16\,\Omega \) wire is bend to form a square loop. A \( 9 \, \text{V} \) supply having internal resistance of \( 1\,\Omega \) is connected across one of its sides. The potential drop across the diagonals of the square loop is ______ \( \times 10^{-1} \, \text{V} \).

The equivalent resistance of the given circuit between the terminals A and B is:

A resistor dissipates \( 192 \, \text{J} \) energy in \( 1 \, \text{s} \) when a current of \( 4 \, \text{A} \) is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in \( 5 \, \text{s} \) is ______ J.

Two cells of emf \( 2E \) and \( E \) with internal resistance \( r_1 \) and \( r_2 \) respectively are connected in series to an external resistor \( R \) (see figure). The value of \( R \), at which the potential difference across the terminals of the first cell becomes zero is:

What equal length of an iron wire and a copper-nickel alloy wire, each of \( 2 \text{mm} \) diameter connected parallel to give an equivalent resistance of \( 3 \Omega \)? (Given resistivities of iron and copper-nickel alloy wire are \( 12 \mu\Omega \text{cm} \) and \( 51 \mu\Omega \text{cm} \) respectively).

In the given figure switches \( S_{1} \) and \( S_{2} \) are in open condition. The resistance across \( ab \) when the switches \( S_{1} \) and \( S_{2} \) are closed is __________ \( \Omega \).

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of \( 15\,\Omega \) resistance is connected across \( BD \). Calculate the current through the galvanometer when a potential difference of \( 10\,\text{V} \) is maintained across \( AC \).

The energy dissipated by a resistor is \( 10 \ \text{mJ} \) in \( 1 \ \text{s} \) when an electric current of \( 2 \ \text{mA} \) flows through it. The resistance is __________ \( \Omega \). (Round off to the Nearest Integer)

A uniform heating wire of resistance \( 36\,\Omega \) is connected across a potential difference of \( 240\,\text{V} \). The wire is then cut into half and a potential difference of \( 240\,\text{V} \) is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be \( 1:x \), where \( x \) is:

For the circuit shown, the value of current at time \( t = 3.2 \, \text{s} \) will be _____ \( \text{A} \).

The voltage drop across \( 15 \, \Omega \) resistance in the given figure will be ________ \( \text{V} \).

In an electric circuit, a cell of certain emf provides a potential difference of \( 1.25 \, \text{V} \) across a load resistance of \( 5 \, \Omega \). However, it provides a potential difference of \( 1 \, \text{V} \) across a load resistance of \( 2 \, \Omega \). The emf of the cell is given by \( \dfrac{x}{10} \, \text{V} \). Then the value of \( x \) is _______.

The voltage across the \( 10 \, \Omega \) resistor in the given circuit is \( x \) volt.

The value of \( x \) to the nearest integer is _______________.

First, a set of \( n \) equal resistors of \( 10 \, \Omega \) each are connected in series to a battery of emf \( 20 \, \text{V} \) and internal resistance \( 10 \, \Omega \). A current \( I \) is observed to flow. Then, the \( n \) resistors are connected in parallel to the same battery. It is observed that the current is increased \( 20 \) times, then the value of \( n \) is ______.

A square shaped wire with resistance of each side \( 3\,\Omega \) is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of \( \Omega \) will be ____________.

In the given figure, a battery of emf \( E \) is connected across a conductor \( PQ \) of length '\( l \)' and different area of cross-sections having radii \( r_{1} \) and \( r_{2} \) \( (r_{2} < r_{1}) \).

If you are provided a set of resistances \( 2 \, \Omega \), \( 4 \, \Omega \), \( 6 \, \Omega \) and \( 8 \, \Omega \). Connect these resistances so as to obtain an equivalent resistance of \( \frac{46}{3} \, \Omega \).

A resistor develops \( 500 \, \text{J} \) of thermal energy in \( 20 \, \text{s} \) when a current of \( 1.5 \, \text{A} \) is passed through it. If the current is increased from \( 1.5 \, \text{A} \) to \( 3 \, \text{A} \), what will be the energy developed in \( 20 \, \text{s} \).

The given potentiometer has its wire of resistance \( 10\,\Omega \). When the sliding contact is in the middle of the potentiometer wire, the potential drop across \( 2\,\Omega \) resistor is:

Consider a \( 72 \, \text{cm} \) long wire \( AB \) as shown in the figure. The galvanometer jockey is placed at \( P \) on \( AB \) at a distance \( x \, \text{cm} \) from \( A \). The galvanometer shows zero deflection. The value of \( x \), to the nearest integer, is:

In the given potentiometer circuit arrangement, the balancing length \( AC \) is measured to be \( 250 \, \text{cm} \). When the galvanometer connection is shifted from point \( (1) \) to point \( (2) \) in the given diagram, the balancing length becomes \( 400 \, \text{cm} \). The ratio of the emf of two cells, \( \dfrac{\varepsilon_1}{\varepsilon_2} \) is :

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

An electric bulb rated as \( 200 \, \text{W} \) at \( 100 \, \text{V} \) is used in a circuit having \( 200 \, \text{V} \) supply. The resistance ‘\( R \)’ that must be put in series with the bulb so that the bulb delivers the same power is ____________ \( \Omega \).

An inductor of \( 10 \, \text{mH} \) is connected to a \( 20 \, \text{V} \) battery through a resistor of \( 10 \, \text{k}\Omega \) and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after \( 1 \, \mu \text{s} \) is \( \dfrac{x}{100} \, \text{mA} \). Then \( x \) is equal to __________________ .
(Take \( e^{-1} = 0.37 \) )

The ratio of the equivalent resistance of the network (shown in figure) between the points \( a \) and \( b \) when switch is closed is \( x : 8 \). The value of \( x \) is _______.

A cylindrical wire of radius \( 0.5 \, \text{mm} \) and conductivity \( 5 \times 10^{7} \, \text{S/m} \) is subjected to an electric field of \( 10 \, \text{mV/m} \). The expected value of current in the wire will be \( x^{3}\pi \, \text{mA} \). The value of \( x \) is ________.

In the given figure, the emf of the cell is \( 2.2 \, \text{V} \) and if internal resistance is \( 0.6 \, \Omega \). Calculate the power dissipated in the whole circuit:

A current of \( 5 \, \text{A} \) is passing through a non-linear magnesium wire of cross-section \( 0.04 \, \text{m}^2 \). At every point the direction of current density is at an angle of \( 60^\circ \) with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: [Resistivity of magnesium \( \rho = 44 \times 10^{-8} \, \Omega \text{m} \) ]

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JEE Main 2021 27th August Evening Shift

The ratio of the equivalent resistance of the network (shown in figure) between the points \( a \) and \( b \) when switch is closed is \( x : 8 \). The value of \( x \) is _______.