The open collector outputs of two$$2$$-inputs $$NAND$$ gates are connected to a common pull up resistor. If the input to the gates are $$P,Q$$ and $$R,S$$ respectively, the output is equal to

In standard $$TTL$$ gates, the totem pole output stage is primarily used to

$$(a)$$ Construct the truth table for the circuit given in Figure $${Q_1},{Q_2}$$ and $${Q_3}$$ are outputs and the clock pulses are the inputs. Unused $$JK$$ inputs are assumed to be at logic $$1.$$ All flip flops are reset at power $$ON$$.
$$(b)$$ Sketch the output waveforms at $${Q_1},{Q_2}$$ and $${Q_3}$$.
$$(c)$$ What function does this circuit perform.

A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$ The locus of the tip of the current phasor, $$I$$, as $$R$$ is varied from $$0$$ to $$\infty $$ is