A potential difference is applied across the filament of a bulb at $t=0,$ and it is maintained at a constant value while the filament gets heated to its equilibrium temperature. We find that the final current in the filament is one-sixth of the current drawn at $t=0.$ If the temperature of the filament at $t=0$ is $20 °\mathrm{C}$ and the temperature coefficient of resistivity at $20 °\mathrm{C}$ is $0.0043 {{}^{\circ }\mathrm{C}}^{-1},$ find the final temperature of the filament.

Determine the voltage drop across the resistor $R_1$ in the circuit given below with $E_1=65 \mathrm{V}$, $R_1=50 \mathrm{\Omega }$, $R_2=100 \mathrm{\Omega }$, $R_3=100 \mathrm{\Omega }$ and $R_4=300 \mathrm{\Omega }$.

A $20 \mathrm{V}$ battery of internal resistance $1 \mathrm{\Omega }$ is connected to three coils of $12 \mathrm{\Omega }$, $6 \mathrm{\Omega }$, and $4 \mathrm{\Omega }$ in parallel, a resistor of $5 \mathrm{\Omega }$ and a reversed battery$\left(EMF 8\hspace{0.17em}V and in ternal resis\tan ce 2\text{Ω}\right)$  as shown in figure.

Calculate,

(a) the current in the circuit,
(b) current in the resistor of $12 \mathrm{\Omega }$ coil and
(c) the potential difference across each battery.

Calculate the resistance between the terminals $A$ and $B$ of the network shown in the figure.

For the resistor network shown in figure, the potential drop between $a$ and $b$ is $12 \mathrm{V}$.

(a) Current through resistance of $6 \mathrm{\Omega }$ is ________.

(b) Current through resistance of $2 \mathrm{\Omega }$ is ________ .

(c) Current through resistance of $8 \mathrm{\Omega }$ is ________ .