In the series $$RC$$ circuit shown in Fig. the voltage across $$C$$ starts increasing when the $$d.c.$$ source is switched on. The rate of increase of voltage across $$C$$ at the instant just after the switch is closed (i.e., at $$t = {0^ + }$$), will be

In the circuit shown in Fig. $$X$$ $$-$$ is an element which always absorbs power. During a particular operation, it sets up a current of $$1$$ $$amp$$ in the direction shown and absorbs a power $${P_{x}}.$$ It is possible that $$X$$ can absorb the same power $${P_x}$$ for another current $$i.$$ Then the value of this current is

A coil (which can be modeled as a series $$RL$$ circuit) has been designed for high $$-$$ $$Q$$ performance at a rated voltage and a specified frequency. If the frequency of operation is doubled, and the coil is operated at the same rated voltage, then the $$Q$$$$-$$factor and the active power $$P$$ consumed by the coil will be affected as follows

An advantage of a permanent magnet moving coil instrument is that it is