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The resistance per centimeter of a meter bridge wire is \( r \), with \( X \, \Omega \) resistance in left gap. Balancing length from left end is at \( 40 \, \text{cm} \) with \( 25 \, \Omega \) resistance in right gap. Now the wire is replaced by another wire of \( 2r \) resistance per centimeter. The new balancing length for same setting will be at:

An electric bulb rated \( 50 \, \text{W} \) – \( 200 \, \text{V} \) is connected across a \( 100 \, \text{V} \) supply. The power dissipation of the bulb is:

At room temperature \( (27^\circ \text{C}) \), the resistance of a heating element is \( 50 \, \Omega \). The temperature coefficient of the material is \( 2.4 \times 10^{-4} \, ^\circ \text{C}^{-1} \). The temperature of the element, when its resistance is \( 62 \, \Omega \) is ......\( ^\circ \text{C} \).

In an ammeter, \( 5\% \) of the main current passes through the galvanometer. If resistance of the galvanometer is \( G \), the resistance of ammeter will be:

Twelve wires each having resistance \( 2\,\Omega \) are joined to form a cube. A battery of \( 6 \,\text{V} \) emf is joined across point \( a \) and \( c \). The voltage difference between \( e \) and \( f \) is _______ \( \text{V} \).

In the given figure an ammeter \( A \) consists of a \( 240 \, \Omega \) coil connected in parallel to a \( 10 \, \Omega \) shunt. The reading of the ammeter is ________ \( \text{mA} \).

A wire of resistance \( R \) and radius \( r \) is stretched till its radius became \( \frac{r}{2} \). If new resistance of the stretched wire is \( xR \), then value of \( x \) is ________.

A galvanometer has a resistance of \( 50\,\Omega \) and it allows maximum current of \( 5\,\mathrm{mA} \). It can be converted into voltmeter to measure upto \( 100\,\mathrm{V} \) by connecting in series a resistor of resistance:

A galvanometer having coil resistance \( 10\,\Omega \) shows a full scale deflection for a current of \( 3 \,\text{mA} \). For it to measure a current of \( 8 \,\text{A} \), the value of the shunt should be:

The electric current through a wire varies with time as \( I = I_0 + \beta t \), where \( I_0 = 20 \, \text{A} \) and \( \beta = 3 \, \text{A/s} \). The amount of electric charge crossed through a section of the wire in \( 20 \, \text{s} \) is:

Two wires A and B are made up of the same material and have the same mass. Wire A has radius of \( 2.0 \, \text{mm} \) and wire B has radius of \( 4.0 \, \text{mm} \). The resistance of wire B is \( 2 \, \Omega \). The resistance of wire A is ____________ \( \Omega \).

A wire of length \( 10 \, \text{cm} \) and radius \( \sqrt{7} \times 10^{-4} \, \text{m} \) connected across the right gap of a meter bridge. When a resistance of \( 4.5 \, \Omega \) is connected on the left gap by using a resistance box, the balance length is found to be at \( 60 \, \text{cm} \) from the left end. If the resistivity of the wire is \( R \times 10^{-7} \, \Omega \, \text{m} \), then value of \( R \) is :

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across \( A \) and \( B \), their readings are \( V_1, V_2 \) and \( V_3 \). Choose the correct option.

Two resistance of \( 100\,\Omega \) and \( 200\,\Omega \) are connected in series with a battery of \( 4\,\text{V} \) and negligible internal resistance. A voltmeter is used to measure voltage across \( 100\,\Omega \) resistance, which give reading as \( 1\,\text{V} \). The resistance of voltmeter must be ______ \( \Omega \).

In the given figure \( R_1 = 10 \, \Omega \), \( R_2 = 8 \, \Omega \), \( R_3 = 4 \, \Omega \) and \( R_4 = 8 \, \Omega \). Battery is ideal with emf \( 12 \, \text{V} \). Equivalent resistant of the circuit and current supplied by battery are respectively:

In the given circuit, the current in resistance \( R_{3} \) is:

In the given circuit, the current flowing through the resistance \( 20 \, \Omega \) is \( 0.3 \, \text{A} \), while the ammeter reads \( 0.9 \, \text{A} \). The value of \( R_1 \) is ________ \( \Omega \).

The value of unknown resistance \( (x) \) for which the potential difference between \( B \) and \( D \) will be zero in the arrangement shown, is:

The ratio of heat dissipated per second through the resistance \( 5 \, \Omega \) and \( 10 \, \Omega \) in the circuit given below is:

The current in a conductor is expressed as \( I = 3t^{2} + 4t^{3} \), where \( I \) is in Ampere and \( t \) is in second. The amount of electric charge that flows through a section of the conductor during \( t = 1 \, \text{s} \) to \( t = 2 \, \text{s} \) is _____ \( \text{C} \).

Two cells are connected in opposition as shown. Cell \( E_1 \) is of \( 8 \, \text{V} \) emf and \( 2 \, \Omega \) internal resistance; the cell \( E_2 \) is of \( 2 \, \text{V} \) emf and \( 4 \, \Omega \) internal resistance. The terminal potential difference of cell \( E_2 \) is ____ \( \text{V} \).

A wire of resistance \( 20 \, \Omega \) is divided into \( 10 \) equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _____ \( \Omega \).

Equivalent resistance of the following network is ________ \( \Omega \).

The effective resistance between \( A \) and \( B \), if resistance of each resistor is \( R \), will be

Resistance of a wire at \( 0^\circ \text{C} \), \( 100^\circ \text{C} \) and \( t^\circ \text{C} \) is found to be \( 10 \, \Omega \), \( 10.2 \, \Omega \) and \( 10.95 \, \Omega \) respectively. The temperature \( t \) in Kelvin scale is ______.

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of \( \frac{1}{\theta} \) vs the resistance \( (R) \) of the resistance box is shown in the figure. The figure of merit of the galvanometer is __________ \( \times 10^{-1} \, \text{A/division} \). [The source has emf \( 2 \, \text{V} \)]

The number of electrons flowing per second in the filament of a \( 110 \, \text{W} \) bulb operating at \( 220 \, \text{V} \) is:
(Given \( e = 1.6 \times 10^{-19} \, \text{C} \))

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are \( 8 \, \Omega \) and \( 10 \, \Omega \) respectively. After inserting in a hot bath of temperature \( 400^\circ \text{C} \), the resistance of platinum wire is:

The reading in the ideal voltmeter \( V \) shown in the given circuit diagram is:

A wire of resistance \( R \) and length \( L \) is cut into \( 5 \) equal parts. If these parts are joined parallely, then resultant resistance will be :

An electric toaster has resistance of \( 60 \, \Omega \) at room temperature \( (27^\circ \, \text{C} \)). The toaster is connected to a \( 220 \, \text{V} \) supply. If the current flowing through it reaches \( 2.75 \, \text{A} \), the temperature attained by toaster is around: \( \big( \text{if } \alpha = 2 \times 10^{-4} / ^\circ \text{C} \big) \)

A galvanometer of resistance \( 100\,\Omega \) when connected in series with \( 400\,\Omega \) measures a voltage of up to \( 10\,\text{V} \). The value of resistance required to convert the galvanometer into ammeter to read up to \( 10\,\text{A} \) is \( x \times 10^{-2}\,\Omega \). The value of \( x \) is:

The current flowing through the \( 1 \, \Omega \) resistor is \( \frac{n}{10} \, \text{A} \). The value of \( n \) is __________.

To determine the resistance \( (R) \) of a wire, a circuit is designed below. the V–I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of \( R \) is ..... \( \Omega \).

In the following circuit, the battery has an emf \( 2 \, \text{V} \) and an internal resistance of \( \dfrac{2}{3} \, \Omega \). The power consumption in the entire circuit is _______ \( \text{W} \).

A potential divider circuit is shown in figure. The output voltage \( V_0 \) is:

In a metre-bridge when a resistance in the left gap is \( 2\,\Omega \) and unknown resistance in the right gap, the balance length is found to be \( 40 \, \text{cm} \). On shunting the unknown resistance with \( 2\,\Omega \), the balance length changes by:

When a potential difference \( V \) is applied across a wire of resistance \( R \), it dissipate energy at a rate \( W \). If the wire is cut into two halve and these halve are connected mutually parallel across the same supply, the energy dissipation rate will become:

To measure the internal resistance of a battery, potentiometer is used. For \( R = 10 \, \Omega \), the balance point is observed at \( l = 500 \, \text{cm} \) and for \( R = 1 \, \Omega \) the balance point is observed at \( l = 400 \, \text{cm} \). The internal resistance of the battery is approximately:

In the given circuit, the terminal potential difference of the cell is:

The deflection in moving coil galvanometer falls from \( 25 \) divisions to \( 5 \) division when a shunt of \( 24 \, \Omega \) is applied. The resistance of galvanometer coil will be:

By what percentage will the illumination of the lamp decrease if the current drops by \( 20\% \)?

Wheatstone bridge principle is used to measure the specific resistance \(( S_1) \) of given wire, having length \( L \), radius \( r \). If \( X \) is the resistance of wire, then specific resistance is; \( S_1 = X \left(\displaystyle \frac{\pi r^{2}}{L} \right) \). If the length of the wire gets doubled then the value of specific resistance will be:

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JEE Main 2024 6th April Morning Shift

A wire of resistance \( R \) and radius \( r \) is stretched till its radius became \( \frac{r}{2} \). If new resistance of the stretched wire is \( xR \), then value of \( x \) is ________.