At $0°\mathrm{C}$, the resistance of a conductor B is $\mathrm{n}$ times that of the conductor $\mathrm{A}.$ The temperature coefficients of $\mathrm{A}$ and $\mathrm{B}$ are ${\mathrm{\alpha }}_1$ and ${\mathrm{\alpha }}_2$ respectively. For the series combination of the two conductors, find the resistance at $0°\mathrm{C}$.

A cell of unknown emf $\epsilon$ and internal resistance r, two unknown resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2\left({\mathrm{R}}_2>{\mathrm{R}}_1\right)$ and a perfect ammeter are given. The current in the circuit is measured in five different situations:

Without any external resistance in the circuit

The current obtained in the five cases are :

$0.42 \mathrm{A}, 0.6 \mathrm{A}, 1.05 \mathrm{A}, 1.4 \mathrm{A}$, and $4.2 \mathrm{A}$

but not necessarily in that order. Identify the currents in the five cases listed above and calculate $\mathrm{E}, \mathrm{r}, {\mathrm{R}}_1$ and ${\mathrm{R}}_2$.

A cell of unknown emf $\epsilon$ and internal resistance r, two unknown resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2\left({\mathrm{R}}_2>{\mathrm{R}}_1\right)$ and a perfect ammeter are given. The current in the circuit is measured in five different situations:

With resistance ${\mathrm{R}}_1$ only

A cell of unknown emf $\epsilon$ and internal resistance r, two unknown resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2\left({\mathrm{R}}_2>{\mathrm{R}}_1\right)$ and a perfect ammeter are given. The current in the circuit is measured in five different situations:

With resistance ${\mathrm{R}}_2$ only

A cell of unknown emf $\epsilon$ and internal resistance r, two unknown resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2\left({\mathrm{R}}_2>{\mathrm{R}}_1\right)$ and a perfect ammeter are given. The current in the circuit is measured in five different situations:

With both ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ used in series combination, and

The current obtained in the five cases are :

$0.42 \mathrm{A}, 0.6 \mathrm{A}, 1.05 \mathrm{A}, 1.4 \mathrm{A}$, and $4.2 \mathrm{A}$

but not necessarily in that order. Identify the currents in the five cases listed above and calculate $\mathrm{E}, \mathrm{r}, {\mathrm{R}}_1$ and ${\mathrm{R}}_2$.

A cell of unknown emf $\epsilon$ and internal resistance r, two unknown resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2\left({\mathrm{R}}_2>{\mathrm{R}}_1\right)$ and a perfect ammeter are given. The current in the circuit is measured in five different situations:

With ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ used in parallel combination.

The current obtained in the five cases are :

$0.42 \mathrm{A}, 0.6 \mathrm{A}, 1.05 \mathrm{A}, 1.4 \mathrm{A}$, and $4.2 \mathrm{A}$

but not necessarily in that order. Identify the currents in the five cases listed above and calculate $\mathrm{E}, \mathrm{r}, {\mathrm{R}}_1$ and ${\mathrm{R}}_2$.