Q: The resistivity of a conductor with a current density of \$2.5 Am\$\$^{-2}\$ when an electric field \$5\times 10^{-8}Vm^{-1}\$ is applied to it, is

\$\textbf{Step 1:}\$ \$\textbf{Relation between Electric field(E), Resistivity and Current density(J)} \$Suppose length of conductor \$ = l\$We know that, Potential difference, \$V=E.l\$\$\textbf{&}\$ Current Density \$J=I/A\$So, \$ I = J A\$and \$ R=\dfrac{\rho l}{A}\$From \$ V = IR\$\$\Rightarrow E.l = J A \times \dfrac{\rho l}{A}\$\$\Rightarrow E = J(\rho)\$\$\therefore \rho = \dfrac{E}{J}\$\$\textbf{Step 2: Putting the values in above equation}\$\$\Rightarrow \rho =\dfrac{E}{J}= \dfrac{5 \times 10^{-8}Vm^{-1}}{2.5Am^2}\$ \$ = 2 \times 10^{-8} \Omega m\$Hence, Option B is correct

Q: The equivalent conductance of two wires of resistance 10 ohm and 5 ohm joined together in parallel is:

Effective resistance of the parallel combination:\$\dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{10}=\dfrac{3}{10}\$So, conductance \$= \dfrac{3}{10}=0.3\$ mho

Q: The resistance between A and B is:

\$ Req \ of \ AC = \dfrac{6\times6}{12} = 3\$\$ Req \ of \ AD = \dfrac{6\times6}{12} = 3\$\$ Req \ of \ AE = \dfrac{6\times6}{12} = 3\$\$ R_{AB} = \dfrac{6\times3}{9} = 2\Omega\$

Question 1

If four resistances are connected as shown in the fig. between A and B, the effective resistance is:

Accepted Answer

Simplified, or equivalent circuit diagram is shown in the figures.From figure, effective resistance:$ R_{eq} = \dfrac{4 \times4}{2 \times 4}$ $ = 2 \Omega$

Question 2

The resistivity of a conductor with a current density  of $2.5 Am$$^{-2}$  when an electric field $5\times 10^{-8}Vm^{-1}$ is applied to it, is

Accepted Answer

$\textbf{Step 1:}$  $\textbf{Relation between Electric field(E), Resistivity and Current density(J)} $Suppose length of conductor $ = l$We know that, Potential difference, $V=E.l$$\textbf{&}$ Current Density $J=I/A$So, $ I = J A$and   $ R=\dfrac{\rho l}{A}$From $ V = IR$$\Rightarrow E.l = J A \times \dfrac{\rho l}{A}$$\Rightarrow E = J(\rho)$$\therefore \rho = \dfrac{E}{J}$$\textbf{Step 2: Putting the values in above equation}$$\Rightarrow \rho =\dfrac{E}{J}= \dfrac{5 \times 10^{-8}Vm^{-1}}{2.5Am^2}$   $ = 2 \times 10^{-8} \Omega m$Hence, Option B is correct

Question 3

A certain piece of copper is to be shaped into a conductor of minimum resistance. Which of the following options will give the minimum resistance?

Accepted Answer

Resistance depends on length and area as follows (resistivity $\rho$ is same in all the cases)$R \propto \dfrac{L}{A}$Case A) $R_A$ $= \rho  \dfrac{L}{A}$Case B) $R_B$ $ = \rho \dfrac{2L}{A}\times2 = \dfrac{\rho L}{A} \times4$Case C) $R_C$ $ = \rho \dfrac{L/2}{2A}=\rho \dfrac{L}{A} \times \dfrac{1}{4}$Case D) $R_D$ $ =\rho \dfrac{3L}{A/3} = \rho \dfrac{L}{A} \times 9$$\Rightarrow$ case $C$ gives minimum resistance.

Question 4

$\text{Assertion(A)} :$ However long a fuse wire may be,the safe current that can be allowed is the same.$\text{Reason (R)} :$ The safe current that can be allowed to pass through a fuse wire depends on the radius of the wire.

Accepted Answer

Both (A) and (R) are both correct but the safe current does not depend on area but on various facts like the material property, temperature, voltage rating etc.hence assertion is correct and reason is correct but reason is not explaining the assertion.

Question 5

The least resistance that one can have from six resistors each of 0.1 ohm resistance is:

Accepted Answer

Least resistance is achieved when all the resistors are connected in parallel.$ \therefore  R_{eq} = \dfrac{R}{6} = \dfrac{0.1}{6} = 0.0167\ \Omega$

Question 6

Three resistances each of $3\Omega $ are connected as shown in figure. The resultant resistance between A and F is:

Accepted Answer

To draw the circuit bring point B to D and Point C to point E. From the diagram, inner two resistances are in parallel,  and its equivalent is also parallel to the third resistance.$\therefore R_{AF} = \dfrac{\dfrac{R}{2} \times R}{\dfrac{3R}{2}}$            $ = \dfrac{R}{3}$$\Rightarrow R_{AF} = 1 \Omega$

Question 7

A wire 50 cm long and $1  \ mm^2$ in cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is

Accepted Answer

By Ohm's law, resistance can be found from current and voltage as below.$ R = \dfrac{V}{I}$    $ = \dfrac{2}{4} = \dfrac{1}{2}  \Omega$The resistance R is dependent on resistivity, length and area of cross-section as below,$ R = \rho \dfrac{l}{A}$$ \Rightarrow  \dfrac{1}{2} = \dfrac{\rho \times 0.50\ m}{{10^{-6}m^2}}$This implies the resistivity of the wire is: $ \Rightarrow   10^{-6}   \Omega m$

Question 8

A wire of resistance $20\Omega $ is bent in the form of a square. The resistance between the ends of diagonal is:

Accepted Answer

Since the wire is bend in form of the square and we know that sides of square are equal so each side will have same resistance i.e 5 ohm. Now if we make diagonal two faces in each side of the diagonal will have two sides and resistance will be 10 ohm.$R=20 \Omega$So, $\dfrac{R}{4}=5 \Omega$$\Rightarrow$ $ R_{1} = 10 \Omega$;  $R_{2} = 10\Omega$So, resistance between the ends of a diagonal = $ R_{D} = \dfrac{10 \times10}{2 \times10}\Omega = 5\Omega$

Question 9

The equivalent conductance of two wires of resistance 10 ohm and 5 ohm joined together in parallel is:

Accepted Answer

Effective resistance of the parallel combination:$\dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{10}=\dfrac{3}{10}$So, conductance $= \dfrac{3}{10}=0.3$ mho

Question 10

The resistance between A and B is:

Accepted Answer

&#10;&#10;&#10;&#9;&#10;&#9;&#10;&#9;&#10;&#9;&#10;&#10;&#10;$ Req  \ &#10;of \   AC = \dfrac{6\times6}{12} = 3$$ Req  \  &#10;of \   AD = \dfrac{6\times6}{12} = 3$$ Req \   of&#10;\   AE  = \dfrac{6\times6}{12} = 3$$ R_{AB} &#10;=  \dfrac{6\times3}{9} = 2\Omega$&#10;&#10;&#10;

Electricity

Physics
7798 Views

If four resistances are connected as shown in the fig. between A and B, the effective resistance is:

The resistivity of a conductor with a current density of $2.5 A m$ $^{- 2}$ when an electric field $5 \times 1 0^{- 8} V m^{- 1}$ is applied to it, is

A certain piece of copper is to be shaped into a conductor of minimum resistance. Which of the following options will give the minimum resistance?

$Assertion(A) :$ However long a fuse wire may be,the safe current that can be allowed is the same.
$Reason (R) :$ The safe current that can be allowed to pass through a fuse wire depends on the radius of the wire.

The least resistance that one can have from six resistors each of 0.1 ohm resistance is:

Three resistances each of $3 Ω$ are connected as shown in figure. The resultant resistance between A and F is:

A wire 50 cm long and $1 m m^{2}$ in cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is

A wire of resistance $20 Ω$ is bent in the form of a square. The resistance between the ends of diagonal is:

The equivalent conductance of two wires of resistance 10 ohm and 5 ohm joined together in parallel is:

The resistance between A and B is:

Electricity

Physics 7798 Views

If four resistances are connected as shown in the fig. between A and B, the effective resistance is:

The resistivity of a conductor with a current density of 2.5Am−2 when an electric field 5×10−8Vm−1 is applied to it, is

A certain piece of copper is to be shaped into a conductor of minimum resistance. Which of the following options will give the minimum resistance?

Assertion(A): However long a fuse wire may be,the safe current that can be allowed is the same. Reason (R): The safe current that can be allowed to pass through a fuse wire depends on the radius of the wire.

The least resistance that one can have from six resistors each of 0.1 ohm resistance is:

Three resistances each of 3Ω are connected as shown in figure. The resultant resistance between A and F is:

A wire 50 cm long and 1 mm2 in cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is

A wire of resistance 20Ω is bent in the form of a square. The resistance between the ends of diagonal is:

The equivalent conductance of two wires of resistance 10 ohm and 5 ohm joined together in parallel is:

The resistance between A and B is:

Physics
7798 Views

The resistivity of a conductor with a current density of $2.5 A m$ $^{- 2}$ when an electric field $5 \times 1 0^{- 8} V m^{- 1}$ is applied to it, is

$Assertion(A) :$ However long a fuse wire may be,the safe current that can be allowed is the same.
$Reason (R) :$ The safe current that can be allowed to pass through a fuse wire depends on the radius of the wire.

Three resistances each of $3 Ω$ are connected as shown in figure. The resultant resistance between A and F is:

A wire 50 cm long and $1 m m^{2}$ in cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is

A wire of resistance $20 Ω$ is bent in the form of a square. The resistance between the ends of diagonal is: