Ohm's Law and Resistance Questions in English

(B) The resistance $R$ of a conductor is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the cross-sectional area.
Rearranging the formula for resistivity,we get $\rho = R \cdot \frac{A}{L}$.
The $SI$ unit of resistance $R$ is Ohm $(\Omega)$,the unit of area $A$ is square meter $(m^2)$,and the unit of length $L$ is meter $(m)$.
Substituting these units into the formula: $\text{Unit of } \rho = \Omega \cdot \frac{m^2}{m} = \Omega \cdot m$.
Therefore,the $SI$ unit of resistivity is $\Omega \cdot m$.

(D) Ohm's law states that the electric current $(I)$ flowing through a metallic conductor is directly proportional to the potential difference $(V)$ across its ends,provided its temperature and other physical conditions remain constant.
Mathematically,this is expressed as $V \propto I$ or $V = IR$,where $R$ is the resistance of the conductor.

(B) Ohm's law states that the current $(I)$ flowing through a conductor is directly proportional to the potential difference $(V)$ applied across its ends,provided the temperature remains constant.
Mathematically,this is expressed as $V = IR$ or $I = V/R$.
Since $V = IR$,the relationship between $V$ and $I$ is linear,meaning the graph of $I$ versus $V$ (or $V$ versus $I$) is a straight line passing through the origin.
Resistance $(R)$ is a constant property of the conductor at a given temperature and does not change with changes in $V$ or $I$.

(C) Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference across its ends,provided the temperature remains constant.
Mathematically,this is expressed as $V \propto I$,which leads to $V = IR$,where $R$ is the resistance of the conductor.
From this formula,we can also derive $R = \frac{V}{I}$ and $I = \frac{V}{R}$.
Option $A$ $(R = \frac{V}{I})$ is a common representation of the definition of resistance derived from Ohm's law,but $V = IR$ is the standard form of the law.

(C) The unit of electrical resistance is the $ohm$ $(\Omega)$.
According to Ohm's Law, $V = IR$, where $V$ is the potential difference in $volts$, $I$ is the current in $amperes$, and $R$ is the resistance in $ohms$.
Therefore, $R = V/I$, which gives the unit as $volt/ampere$, defined as $ohm$.

(D) The unit of electrical resistance is the ohm.
It is denoted by the Greek letter omega,represented by the symbol $\Omega$.
$R$ is the symbol for resistance itself.
$I$ is the symbol for electric current.
$\rho$ (rho) is the symbol for electrical resistivity.

(D) Insulators are materials that do not allow the flow of electric current through them.
This is because they have a very high electrical resistance,which prevents the movement of free electrons.
Therefore,the resistance of insulating materials is very large compared to conductors.

(A) Resistors used in electronic devices like radios and televisions are typically carbon resistors.
These are made from a mixture of carbon and graphite,which acts as the resistive material,often bound with a ceramic or plastic material.
Carbon resistors are preferred in these applications due to their small size,low cost,and ability to handle high-frequency signals effectively.

(D) The resistance $R$ of a conductor is given by the formula $R = \rho \frac{l}{A}$,where:
$1$. $\rho$ (rho) is the resistivity,which depends on the nature of the material.
$2$. $l$ is the length of the conductor.
$3$. $A$ is the area of cross-section.
Since the resistance depends on all these three factors,the correct option is $D$.

(C) The resistance $R$ of a conducting wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the cross-sectional area of the wire.
From this relation,it is clear that resistance is inversely proportional to the cross-sectional area $(R \propto \frac{1}{A})$.
If the area $A$ is doubled $(A' = 2A)$,the new resistance $R'$ becomes $R' = \rho \frac{L}{2A} = \frac{1}{2} R$.
Therefore,the resistance becomes half of its original value.

(D) The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is resistivity,$L$ is length,and $A$ is the cross-sectional area.
Since the wire is cylindrical,the cross-sectional area $A = \pi r^2$,where $r$ is the radius.
Since the diameter $D = 2r$,we can write $A = \pi (D/2)^2 = \frac{\pi D^2}{4}$.
Substituting this into the resistance formula: $R = \rho \frac{L}{\pi D^2 / 4} = \frac{4 \rho L}{\pi D^2}$.
This shows that $R \propto \frac{1}{D^2}$.
If the diameter $D$ is doubled $(D' = 2D)$,the new resistance $R'$ becomes $R' = \frac{4 \rho L}{\pi (2D)^2} = \frac{4 \rho L}{4 \pi D^2} = \frac{1}{4} R$.
Therefore,the resistance becomes one-fourth of its original value.

(A) According to Ohm's Law,the electric current flowing through a metallic conductor is directly proportional to the potential difference $(V)$ applied across its ends,provided its temperature remains constant.
Mathematically,this is expressed as $V \propto I$,which leads to $V = IR$ or $\frac{V}{I} = R$.
Here,$R$ is a constant for the given metallic conductor at a given temperature and is known as its resistance.
Resistance is the property of a conductor to resist the flow of charges through it.

(B) The resistivity of a material is a fundamental property that quantifies how strongly a given material opposes the flow of electric current.
It is denoted by the Greek letter $\rho$ (rho).
The $SI$ unit of resistivity is the ohm-meter $(\Omega \cdot m)$.
In contrast,$R$ represents resistance,and $\Omega$ is the symbol for the unit ohm.

(D) The resistivity $(\rho)$ of materials is a measure of how strongly a material opposes the flow of electric current.
Materials are classified based on their resistivity as follows:
$1$. Conductors: Have very low resistivity (e.g., metals like copper, silver).
$2$. Insulators: Have very high resistivity (e.g., glass, rubber).
$3$. Semiconductors: Have resistivity values that lie between those of conductors and insulators (e.g., silicon, germanium).
Therefore, the resistivity of semiconductors is greater than that of conductors but less than that of insulators.

(B) According to Ohm's law,the relationship between voltage $(V)$,current $(I)$,and resistance $(R)$ is given by the formula: $V = I \times R$.
Given values are:
Current $(I)$ = $0.5\, A$
Resistance $(R)$ = $440\, \Omega$
Substituting these values into the formula:
$V = 0.5\, A \times 440\, \Omega$
$V = 220\, V$
Therefore,the electric bulb should be connected to a $220\, V$ line.

(A) According to Ohm's Law,the relationship between voltage $(V)$,current $(I)$,and resistance $(R)$ is given by the formula $V = I \times R$.
Given values are:
Voltage $(V)$ = $120\;V$
Current $(I)$ = $2\;A$
To find the resistance $(R)$,we rearrange the formula: $R = V / I$.
Substituting the values: $R = 120\;V / 2\;A = 60\;\Omega$.
Therefore,the resistance of the heater coil is $60\;\Omega$.