Electric Current

To solve the given problem, let's analyze the electrical circuit and the components' behavior under the conditions mentioned.

First, we need to understand the setup:

• An electrical circuit with a voltmeter and an ammeter is given. The objective is to determine the readings on these devices.

We'll break the analysis into key steps:

The current flowing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant. This is given by the formula:

where is the current, is the voltage, and is the resistance.

In many exam questions, voltmeters are assumed to be ideal and have infinite resistance, meaning they draw no current, and ammeters have zero resistance and do not affect the circuit's current.

In the given problem, we understand that:

• If the voltagemeter reading is 0 V, the points it is connected across are at the same potential.
• If the ammeter reads 2 A, current flows as stated; this implies a closed path that allows current flow without any potential difference across other points it measures.

Given the options and the correct answer

0 V, 2 A

1. , it indicates:

• The voltmeter reading of confirms no potential difference across the specified points.
• The ammeter reading of indicates the circuit allows for this flow. This rules out scenarios of open circuits or misconnected paths, validating the circuit's completeness and functioning.

Thus, the correct readings from the circuit as per the problem's context and logic are indeed: 0 V, 2 A.

Step 1: Analyze each statement based on energy considerations in an electrical conductor.

The potential difference causes charge to move, resulting in work done by the electric field. The work done is . Since , . So, Work done = .

(I) The kinetic energy of the charge increases by .
This is False. In a conductor, electrons accelerate due to the electric field, but they collide with the lattice ions, losing this kinetic energy. The drift velocity and hence average kinetic energy remain constant.

(II) The electric potential energy of the charge decreases by .
This is True. When a positive charge moves from a higher potential to a lower potential, or a negative charge moves from a lower potential to a higher potential, electric potential energy decreases. Here, the charge is moving through a potential difference , so the potential energy decreases by .

(III) The thermal energy of the conductor increases by .
This is True. The energy lost in potential energy is converted into heat due to collisions of electrons with the atoms in the conductor lattice. This increases the thermal energy of the conductor.

Step 2: Identify the correct statement(s).

Statements (II) and (III) are correct.

Answer 28: (D) (II), (III)

Wire-bound resistors are typically made by winding the wire of an alloy of Manganin, Constantan, and Nichrome.

Manganin is an alloy composed of copper, manganese, and nickel. It has a low temperature coefficient of resistance, meaning its resistance changes very little with temperature variations. Manganin is often used for precision resistors due to its stability in varying temperature conditions.

Constantan is another copper-based alloy made of copper and nickel. It has a relatively high resistivity and is commonly used in resistors because of its stable resistance over a wide temperature range.

Nichrome is a nickel-chromium alloy that is known for its high electrical resistivity. It is often used in heating elements and resistors where high-temperature applications are required due to its ability to withstand elevated temperatures.

Therefore, the correct answer is: (C) wire-bound resistors are made by winding the wire of an alloy of Manganin, Constantan, and Nichrome.

We are given 10 identical cells, each with electromotive force (EMF) 'E' and internal resistance 'r'.

These cells are connected in series to form a closed circuit. This means the positive terminal of the last cell is connected to the negative terminal of the first cell, forming a loop.

1. Calculate the total EMF and total internal resistance for the closed circuit:

Since the 10 cells are in series:

• Total EMF:
• Total internal resistance:

2. Calculate the current flowing in the closed circuit:

Using Ohm's law for the complete circuit (where the external resistance is zero):

This is the current flowing through each cell in the closed loop.

3. Determine the voltmeter reading across three cells:

An ideal voltmeter measures the potential difference (terminal voltage) between the two points it is connected across. It is connected across three cells in series.

The combined EMF of these three cells is .

The combined internal resistance of these three cells is .

The potential difference across the terminals of these three cells while the current is flowing is given by:

Now, substitute the value of the current we calculated for the closed circuit:

According to this calculation, based on the description "formed a closed circuit", the reading of the ideal voltmeter should be 0.

4. Reconsidering the options:

The calculated value of 0 is not among the given options (13E, 10E, 7E, 3E). This suggests a possible ambiguity or error in the question statement or the options provided.

Often in such scenarios, if the circuit were open (meaning no current flows, ), the voltmeter would measure the total EMF of the cells it spans.

If we assume the circuit is open or that the question implicitly asks for the combined EMF of the three cells (despite connecting a voltmeter which measures potential difference), then:

This value (3E) matches one of the options.

Conclusion based on options:

Given the discrepancy between the calculation for a "closed circuit" (V=0) and the provided options, the most likely intended answer, corresponding to option 3E, assumes either an open circuit condition ( ) or that the question is simply asking for the total EMF of the three cells.

Given Information:
Galvanometer resistance,
Shunt resistance,
Ammeter range,
Number of divisions on one side = divisions

Step-by-Step Explanation:

Step 1: Find the galvanometer current ( ) for full-scale deflection.

Using the formula for shunt resistance in galvanometer conversion:

Substitute given values:

Solving for :

Bring terms involving together:

Thus,

Step 2: Find current sensitivity (divisions per ampere):

Number of divisions for full-scale deflection = divisions

Thus, current sensitivity ( ) is:

Final Conclusion:
Current sensitivity is .