In the figure a part of circuit is shown : 

  

Find the current flowing through the resistance $R_1$ of the circuit shown in figure if the resistances are equal to $R_1=10 \mathrm{\Omega }, R_2=20 \mathrm{\Omega }$, and $R_3=30 \mathrm{\Omega }$, and the potentials of points $1, 2$ and $3$ are equal to ${\mathrm{\phi }}_1 = 10 \mathrm{V}, {\mathrm{\phi }}_2 = 6 \mathrm{V},$ and ${\mathrm{\phi }}_3 = 5 \mathrm{V}$.

In the circuit shown in figure if the resistances are equal to $R_1=10 \mathrm{\Omega }, R_2=20 \mathrm{\Omega }$, and $R_3=30 \mathrm{\Omega }$, and the potentials of points $1, 2$ and $3$ are equal to ${\mathrm{\phi }}_1 = 10 \mathrm{V}, {\mathrm{\phi }}_2 = 6 \mathrm{V},$ and ${\mathrm{\phi }}_3 = 5 \mathrm{V}$.

In the figure shown the current flowing through $2 R$ is :

Find the current through the $10 \mathrm{\Omega }$ resistor shown in figure

Two coils connected in series have resistances $600 \mathrm{\Omega }$ and $300 \mathrm{\Omega }$ at $20°\mathrm{C}$ and temperature coefficient of resistivity $0.001{ \mathrm{K}}^{-1}$ and $0.004{ \mathrm{K}}^{-1}$ respectively.

(a) The resistance of the combination at temperature $50°\mathrm{C}$ is

Two coils connected in series have resistances $600 \mathrm{\Omega }$ and $300 \mathrm{\Omega }$ at $20°\mathrm{C}$ and temperature coefficient of resistivity $0.001{ \mathrm{K}}^{-1}$ and $0.004{ \mathrm{K}}^{-1}$ respectively.

(b) The effective temperature coefficient of the combination is

In the ladder network shown, current through the resistor $3 \mathrm{\Omega }$ is $0.25 \mathrm{A}$. The input voltage $‘\mathrm{V}’$ is equal to