A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is mid-point of arm $CD$ )
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$A$ wire of cross-section area $A$, length $L_1$, resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$, resistivity $\rho_2$ , temperature coefficient of resistivity $\alpha_1$ and the same area $A$, so that wire carries same current. Total resistance $R$ is independent of temperature for small temperature change if (Thermal expansion effect is negligible)
The heating coils rating at $220\, volt$ and producing $50\, cal/sec$ heat are available with the resistances $55\,\Omega $ , $110\,\Omega$ , $220\,\Omega $ and $440\,\Omega $. The heater of maximum power will be of............. $\Omega$
The current $i_1$ and $i_2$ through the resistor $R_1 (= 10\,\Omega )$ and $R_2 (=30 \,\Omega )$ in the circuit diagram with $E_1 = 3\,V, E_2 = 3\,V$ and $E_3 = 2\,V$ are respectively: