The inductance of a long solenoid of length $$1000$$ $$mm$$ wound uniformly with $$3000$$ turns on a cylindrical paper tube of $$60$$ $$mm$$ diameter is

The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______.

A bipolar junction transistor $$(BJT)$$ is used as a power control switch by biasing it in the cut-off region (OFF state) or in the saturation region (ON state). In the ON state, for the $$BJT.$$

The triggering circuit of a thyristor is shown in figure. The thyristor requires a gate current of $$10$$ $$mA,$$ for guaranteed turn-on. The value of $$R$$ required for the thyristor to turn on reliably under all conditions of $${V_b}$$ variation is