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Read the passage given below and then answer questions on the basis of your under standing of the passage and the related studied concepts. Passage: When a resistor is connected across the terminals of a battery, a current is established in the circuit which has a unique direction going from positive terminal to the negative terminal via the external resistor. Magnitude of the current also remains practically constant. If the direction of the current in a resistor (or any other element) changes alternately, the current is called an alternating current. The alternating current being supplied in our houses varies sinusoidally with time. Such a current repeats its value after a finite time interval T, called the time period. So, the current is positive for one half period and is negative for the remaining half period. In reality it means that direction of current reverses after every half time period. An alternating current may be expressed asI = I_(w) sin (omega t + phi) where I_(m)is the peak value of current or the current amplitude. The mean current for a period T is definitely zero but mean of I^(2) over the same period is not zero because I^(2)is always positve. The average of l^(2)over a time period T or a long period of time isl_(m)^(2) = l_(m)^(2)/2 . The square root of mean square current is called rms current or virtual current and it is given asI_(rms) = I_(m)/sqrt(2) (b) Two alternating currents are expressed as I_(1) = I_(m) sin (omegat + phi) and I_(2) = I_(m) cos (omega t + phi). What is the difference between the two currents? |
| Answer» Solution :`I_(2)` and `I_(2)` have dame peak value, PERIOD (or frequency) but `I_(2)` is ahead phase by `pi/2` as compared to `I_(1)` as `I_(2)` MAY be expressed as `I_(2) = I_(m) COS (omega t + phi) = I_(m) SIN (omega t + phi + pi/2)` | |