Chapter: Electricity and Magnetism
In an electric circuit, a wire of resistance 10 W is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :
The resistance \( R \) of a wire is given by the formula:
Where \( R \) is resistance, \( \rho \) is resistivity, \( L \) is length, and \( A \) is cross-sectional area.
Initially, the resistance \( R_1 \) of the wire is:
When the wire is stretched to double its length \( L' = 2L \), the new area \( A' \) decreases as:
Thus, the new resistance \( R_2 \) becomes:
Substituting \( R_1 \):
For current \( I \), we know:
Thus, the new current \( I' \) can be expressed as:
The current thus decreases to one-fourth of its original value.
Remember: Doubling the length quadruples the resistance leading to a quarter in current.
A schematic representation showing a wire with initial length and resistance, followed by arrows indicating stretching to double its length, illustrating the corresponding increase in resistance and decrease in current. Labeling should clearly denote initial and stretched states.
Verified against NCERT Class XII Physics, Chapter 12 (Current Electricity).
The work done in moving a charge of 2 coulombs( C) from point A to point B is 24 J. What is the potential difference between A and B?
Option C is correct. [The potential difference is 12 V.]
Potential difference (V) quantifies the work done per unit charge moved between two points in an electric field.
Remember, V = W/Q helps quickly determine potential differences in electric problems.
V = W/Q defines the relationship between work and potential difference for electric charges.
Which one of the following statements regarding Ohm's law is not correct?
Ohm's Law states that the current (\(I\)) through a conductor between two points is directly proportional to the voltage (\(V\)) across the two points, and this is mathematically expressed as:
Where \(R\) is the constant resistance.
Ohm's Law applies under certain conditions. Specifically:
Option (a): Correctly indicates that Ohm's law is a fundamental assumption about the relationship between voltage and current.
Option (b): Correctly notes that a device must have a constant resistance to obey Ohm's law.
Option (c): Correctly states that resistance should not be dependent on the applied field for Ohm's law to hold.
Option (d): Is incorrect because it generalizes that all materials obey Ohm's law regardless of field strength.
Remember: "Ohm's law holds where voltage and current flow linearly within limits." Use "V = IR" to keep it succinct.
Verified against NCERT Class 12 Physics, Chapter 12 (Electrical Conductors).
“The sum of emf's and potential differences around a closed loop equals zero” is a consequence of
The statement “The sum of emf's and potential differences around a closed loop equals zero” is a representation of the Conservation of Energy.
The governing equation can be expressed as:
This implies:
Where:
This relationship ensures that all energy supplied in the circuit equals the energy used, upholding the principle of energy conservation.
Remember: “E is all I need” to associate energy conservation with emf and potential differences in circuits.
Verified against NCERT Class XII Physics, Chapter 6 (Electromagnetic Induction).
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