An infinite ladder network of resistors is shown in the figure. If $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$,then the equivalent resistance between $A$ and $B$ is ................ $\Omega$.

Refer to the circuit shown. What will be the total power dissipation in the circuit if $P$ is the power dissipated in $R_1$ (in $P$)? It is given that $R_2 = 4 R_1$ and $R_3 = 12 R_1$.

The reading of the ammeter as per the figure shown is:

Two resistances of $400 \Omega$ and $800 \Omega$ are connected in series with a $6 \text{ V}$ battery of negligible internal resistance. $A$ voltmeter of resistance $10000 \Omega$ is used to measure the potential difference across the $400 \Omega$ resistor. The error in the measurement of potential difference in volts is approximately:

Three identical batteries are connected in series with a wire of length $L$. The temperature of the wire increases by $T$ in time $t$. If $N$ such batteries are connected in series with a wire of the same material but length $2L$,the temperature increases by the same amount $T$ in the same time $t$. Find the value of $N$.

The neutral temperature of a thermocouple is defined as the temperature at which: