Question

Column I gives physical quantities based on a situation in which an ideal cell of emf $V$ is connected across a cylindrical rod of uniform cross-section area and conductivity $\left(\sigma \right)$ as shown in figure. $E,J,\varphi$ and $i$ are electric field at, current density through, electric flux through and current through shaded cross-section respectively as shown in figure. Match the expression in Column I with the statements in Column II.

$\begin{array}{cccc}& \text{Column -I}& & \text{Column-II}\\ \text{(A)}& \frac{\varphi }{i}& \text{(P)}& \text{Conductivity of rod}\\ \text{(B)}& \frac{E}{J}& \text{(Q)}& \text{Resistance of rod}\\ \text{(C)}& \sigma \varphi V& \text{(R)}& \text{Resistivity of rod}\\ \text{(D)}& \frac{V}{\sigma phi}& \text{(S)}& \text{Power delivered to rod}\end{array}$
Which of the following is the only CORRECT combination ?

• A. $\text{(A)}\to \text{R};\text{(B)}\to \text{R};\text{(C)}\to \text{S};\text{(D)}\to \text{Q}$
• B. $\text{(A)}\to \text{S};\text{(B)}\to \text{Q};\text{(C)}\to \text{P};\text{(D)}\to \text{R}$
• C. $\text{(A)}\to \text{P};\text{(B)}\to \text{P};\text{(C)}\to \text{Q};\text{(D)}\to \text{S}$
• D. $\text{(A)}\to \text{Q};\text{(B)}\to \text{S};\text{(C)}\to \text{R};\text{(D)}\to \text{P}$

Answer 1

The correct option is A $\text{(A)}\to \text{R};\text{(B)}\to \text{R};\text{(C)}\to \text{S};\text{(D)}\to \text{Q}$

We know the relation between given quantities is $\varphi =EAi=JAE=J\rho \sigma =\frac{1}{\rho }V=ELP=\frac{V^2}{R},R=\frac{\rho L}{A}$



A) $\frac{\varphi }{i}=\frac{E.A}{JA}=\frac{E}{J}=\rho$

B) $\frac{E}{J}=\rho$

c) $\sigma \varphi V=\frac{\varphi V}{\rho }=\frac{EAV}{\rho }=\frac{V^{2}A}{\rho L}=\frac{V^2}{R}=P$

d) $\frac{V}{\sigma \varphi }=\frac{V\rho }{\varphi }=\frac{EL\rho }{EA}=R$