$10$ wires (same length,same area,same material) are connected in parallel and each has $1 \ \Omega$ resistance,then the equivalent resistance will be .............. $\Omega$.

An electric heater and an electric bulb are rated $500\, W, 220\, V$ and $100\, W, 220\, V$ respectively. Both are connected in series to a $220\, V$ $a.c.$ mains. The current in the circuit when both are connected in series is ................ $A$.

$A$ wire of resistance $R$ is bent into a circular ring of radius $r$. The equivalent resistance between two points $X$ and $Y$ on its circumference,where the central angle $XOY$ is $\alpha$ (in radians),is given by:

Find the equivalent resistance between points $A$ and $B$.

Two wires with temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ have resistances $R_1$ and $R_2$ at $0^{\circ}C$. If they are connected in series,what is the effective temperature coefficient of resistance?

$A$ copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance