A resistance thermometer measures temperature with the increase in resistance of a wire of high temperature. If the wire is platinum and has a resistance of $10 \mathrm{\Omega }$ at $20 °\mathrm{C}$ and resistance of $35 \mathrm{\Omega }$ in a hot furnace, what is the temperature of the furnace? $\left({\alpha }_{\text{platinum }}=0.0036 °{\mathrm{C}}^{-1}\right)$

(a) At what temperature would the resistance of a copper conductor be double its value of $0°\mathrm{C}?$

(b) Does this same temperature hold for all copper conductors, regardless of shape and size? $\left[{\alpha }_{\mathrm{C}}=4.0\times {10}^{-3}{ °\mathrm{C}}^{-1}\right]$

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.