A zener diode having zener voltage $8 V$ and power dissipation rating of $0.5 W$ is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance $R_p$ is _____$\mathrm{\Omega }.$

 

In the given figure switches $S_1$ and $S_2$ are in open condition. The resistance across $ab$ when the switches $S_1$ and $S_2$ are closed is ________$\mathrm{\Omega }.$

A Copper $\left(\mathrm{Cu}\right)$ rod of length $25 \mathrm{cm}$ and cross-sectional area $3{ \mathrm{mm}}^2$ is joined with a similar Aluminium $\left(\mathrm{Al}\right)$ rod as shown in figure. Find the resistance of the combination between the ends $A$ and $B.$

(Take resistivity of Copper $=1.7\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$, Resistivity of aluminium $=2.6\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$)

In the given figure, there is a circuit of potentiometer of length $AB=10 \mathrm{m}$. The resistance per unit length is $0.1 \mathrm{\Omega }$ per $\mathrm{cm}$. Across $AB$, a battery of emf $E$ and internal resistance $r$ is connected. The maximum value of emf measured by this potentiometer is:

In the given potentiometer circuit arrangement, the balancing length $\mathrm{AC}$ is measured to be $250 \mathrm{cm}$. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes $400 \mathrm{cm}$. The ratio of the emf of two cells $\frac{{\epsilon }_1}{{\epsilon }_2}$ is:

The given potentiometer has its wire of resistance $10 \mathrm{\Omega }$. When the sliding contact is in the middle of the potentiometer wire, the potential drop across $2 \mathrm{\Omega }$ resistor is: