The smallest temperature difference that can be measured with a combination of a thermocouple of thermo $e.m.f.$ $30\,\mu V$ per degree and a galvanometer of $50\,\Omega$ resistance,capable of measuring a minimum current of $3 \times 10^{-7} \, A$ is ............... $^\circ C$.

If the heat produced in the $5 \, \Omega$ resistor is $10 \, \text{cal/sec}$, then how much heat in $\text{cal/sec}$ is produced in the $4 \, \Omega$ resistor?

An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it,its resistance at room temperature $(27.0^{\circ} C)$ is found to be $75.3\; \Omega$. When the toaster is connected to a $230\; V$ supply,the current settles,after a few seconds,to a steady value of $2.68\; A$. What is the steady temperature (in $^{\circ} C$) of the nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range involved is $1.70 \times 10^{-4}\; ^{\circ} C^{-1}$.

In an experiment on a circuit as shown in the figure, the voltmeter shows $8 \,V$ reading. The resistance of the voltmeter is,

Find the potential difference between $a$ and $b$,as shown in the below circuit. (in $V$)

As shown,the circuit is made of $8$ different resistors. It is found that when $R_1 = 4\,\,\Omega,$ the resistance between $A$ and $B$ is $2\,\,\Omega.$ Now replace $R_1$ by a $6\,\,\Omega$ resistor,what is the resistance between $A$ and $B$?