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For the two cells having same EMF \( E \) and internal resistance \( r \), the current passing through the external resistor \( 6\,\Omega \) is same when both the cells are connected either in parallel or in series. The value of internal resistance \( r \) is __________ \( \Omega \).

Refer to the circuit diagram given below. The heat generated across the \( 6\Omega \) resistance in \( 100 \) second is \( \dfrac{\alpha}{100} \, \text{J} \). The value of \( \alpha \) is ______. (Nearest integer)

A moving coil galvanometer of resistance \( 100 \, \Omega \) shows a full scale deflection for a current of \( 1 \, \text{mA} \). The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of \( 5 \, \text{mA} \), is ____________ \( \Omega \).

Two resistors \( 2\,\Omega \) and \( 3\,\Omega \) are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire \( XY \). When an unknown resistor is connected in parallel with \( 3\,\Omega \) resistor, the null point is shifted by \( 22.5 \,\text{cm} \) toward \( Y \). The resistance of unknown resistor is ______ \( \Omega \).

Two cells of emfs \( 1 \, \text{V} \) and \( 2 \, \text{V} \) and internal resistance \( 2 \, \Omega \) and \( 1 \, \Omega \), respectively connected in parallel, gave a current of \( 1 \, \text{A} \) through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be \( \dfrac{\alpha}{5} \, \text{A} \). The value of \( \alpha \) is __________.

Two known resistances of \( R\,\Omega \) and \( 2R\,\Omega \) and one unknown resistance \( x\,\Omega \) are connected in a circuit as shown in the figure. If the equivalent resistance between points \( A \) and \( B \) in the circuit is \( x\,\Omega \), then the value of \( x \) is _______ \( \Omega \).

When an external resistance of \( 5 \, \Omega \) is connected across terminals of a cell, a current of \( 0.25 \, \text{A} \) flows through it. When the \( 5 \, \Omega \) resistor is replaced by a \( 2 \, \Omega \) resistor, a current of \( 0.5 \, \text{A} \) flows through it. The internal resistance of the cell is ___________ \( \Omega \).

A meter bridge with two resistances \( R_1 \) and \( R_2 \) as shown in figure was balanced (null point) at \( 40 \) cm from the point \( P \). The null point changed to \( 50 \) cm from the point \( P \), when \( 16\,\Omega \) resistance is connected in parallel to \( R_2 \). The Q. values of resistances \( R_1 \) and \( R_2 \) are __________.

Refer to the figure given blow. The values of \( I_1, I_2 \) and \( I_3 \) are ______.

In a meter bridge experiment to determine the value of unknown resistance, first the resistance \( 2 \, \Omega \) and \( 3 \, \Omega \) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \( l \) cm from the left. Now when an unknown resistance \( x \, \Omega \) is connected in parallel to \( 3 \, \Omega \) resistance, the null point is shifter by \( 10 \, \text{cm} \) to the right of wire. The value of unknown resistance \( x \) is ________________ \( \Omega \).

A wire of uniform resistance \( \lambda \, \Omega / \text{m} \) is bent into a circle of radius \( r \) and another piece of wire with length \( 2r \) is connected between points A and B (AOB) as shown in figure. The equivalent resistance between points A and B is ______ \( \Omega \).

Refer of the figure given below, current between terminals \( A \) and \( B \) is ______ \( \text{A} \).

A voltmeter with internal resistance of \( x \, \Omega \) can be used to measure upto \( 20 \, \text{V} \). In order to increase its measuring range to \( 30 \, \text{V} \), the required modification is to ________.

A regular hexagon is formed by six wires each of resistance \( r \, \Omega \) and the corners are joined to the center by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be:

A cylindrical conductor of length \( 2 \, \text{m} \) and area of cross-section \( 0.2 \, \text{mm}^{2} \) carries an electric current of \( 1.6 \, \text{A} \) when its ends are connected to a \( 2 \, \text{V} \) battery. Mobility of electrons in the conductor is \( \alpha \times 10^{-3} \, \text{m}^{2}/(\text{V s}) \). The value of \( \alpha \) is: (electron concentration \( = 5 \times 10^{28} \, \text{m}^{3} \) and electron charge \( = 1.6 \times 10^{-19} \, \text{C} \))

The equivalent resistance between the points \( A \) and \( B \) in the following circuit is \( \frac{x}{5} \, \Omega \). The value of \( x \) is ________.

In the potentiometer, when the cell in the secondary circuit is shunted with \( 4\Omega \) resistance, the balance is obtained at the length \( 120 \, \text{cm} \) of wire. Now when the same cell is shunted with \( 12\Omega \) resistance, the balance is shifted to a length of \( 180 \, \text{cm} \). The internal resistance of cell is ________ \( \Omega \).

The voltage and the current between \( A \) and \( B \) points shown in the circuit are ______.

Two resistors of \( 200\,\Omega \) and \( 400\,\Omega \) are connected in series with a battery of \( 100 \, \text{V} \). A bulb rated at \( 200 \, \text{V}, 100 \, \text{W} \) is connected across the \( 400\,\Omega \) resistance. The potential drop across the bulb is _______ \( \text{V} \).

The heat generated in \( 1 \, \text{minute} \) between points \( A \) and \( B \) in the given circuit, when a battery of \( 9 \, \text{V} \) with internal resistance of \( 1 \, \Omega \) is connected across these points is __________________\( \text{J} \).

Two resistors of \( 100 \, \Omega \) each are connected in series with a \( 9 \, \text{V} \) battery. A voltmeter of \( 400 \, \Omega \) resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ______ \( \text{V} \).

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JEE Main 2026 4th April Morning Shift

A voltmeter with internal resistance of \( x \, \Omega \) can be used to measure upto \( 20 \, \text{V} \). In order to increase its measuring range to \( 30 \, \text{V} \), the required modification is to ________.