Current Electricity

Finding the Resistance of the Bulb:
We know that the power consumed by the bulb is given by the formula:
where:
- is the power,
- is the voltage,
- is the resistance.
Rearranging the equation to solve for :

Substitute the given values:

Thus, the resistance of the bulb is .
Finding the rms Current Through the Bulb:
The rms (root mean square) current is related to the power and voltage by the formula:

Rearranging the equation to solve for :

Substitute the known values:

Thus, the rms current through the bulb is approximately .

a. Resistance of 100 watt and 400 watt Bulbs:
The power consumed by an electrical device is related to the voltage and resistance by the formula:

Rearranging the equation to solve for :

Since both bulbs have the same voltage, we can compare their resistances using their respective power ratings.
For the 100 watt bulb:

For the 400 watt bulb:

Thus, the resistance of the 100 watt bulb is four times the resistance of the 400 watt bulb. Therefore:

So, the resistance of the 100-watt bulb is four times greater than the resistance of the 400-watt bulb.
b. Resistance Change with Length and Area:
The resistance of a wire is given by the formula:

where:
- is the resistivity of the material,
- is the length of the wire,
- is the cross-sectional area of the wire.
When the length of the wire is halved and the area is doubled, we can substitute these changes into the formula.
New length =
New area =
The new resistance will be:

Thus, the new resistance will be one-fourth of the original resistance.

a. Differences Between Electromotive Force (emf) and Potential Difference (pd):
1. Definition:
- Electromotive Force (emf): emf is the energy supplied by a source (such as a battery or generator) per unit charge to move charges through a circuit. It is responsible for driving the current in the circuit.
- Potential Difference (pd): pd is the difference in electric potential between two points in a circuit. It represents the energy required to move a unit charge between two points in the circuit.
2. Cause:
- Electromotive Force (emf): It is caused by an energy source like a battery or generator, where chemical, mechanical, or thermal energy is converted into electrical energy.
- Potential Difference (pd): pd is caused by the resistance in the circuit and represents the work done by the electric field to move charges.
3. Measurement:
- Electromotive Force (emf): emf is measured in volts (V), and it is the work done per unit charge to move the charge through the complete circuit (when no current is flowing).
- Potential Difference (pd): pd is also measured in volts (V), and it is the work done per unit charge between two points in a closed circuit (when current is flowing).
b. Differences Between Resistance and Specific Resistance:
1. Definition:
- Resistance (R): Resistance is the opposition that a material offers to the flow of electric current. It depends on the material, shape, and size of the conductor.
- Specific Resistance (Resistivity, ): Specific resistance, or resistivity, is a property of the material that quantifies its intrinsic resistance to electric current. It is independent of the size and shape of the conductor.
2. Formula:
- Resistance (R): The formula for resistance is given by , where is the length of the conductor, is the cross-sectional area, and is the specific resistance (resistivity).
- Specific Resistance (Resistivity, ): Resistivity is represented by , where is the resistance, is the area, and is the length of the conductor.
3. Units:
- Resistance (R): The unit of resistance is ohms ( ).
- Specific Resistance (Resistivity, ): The unit of specific resistance is ohm-meter ( ).

As temperature increases, the drift velocity of electrons decreases because the increase in thermal motion of atoms causes more collisions with free electrons.

A galvanometer is converted into a voltmeter by adding a large resistance (called a series resistor) in series with it.

The sensitivity of a galvanometer is reduced by the use of a shunt resistor, as it divides the current between the galvanometer and the shunt.

Direct current (DC) is a constant current, which has no frequency. Thus, the frequency of a direct current is zero.