3400 4 200 82 ee1002introductiontocircuitsandsystems

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Unformatted text preview: known as the root‐mean‐square (RMS) value of the voltage signal. The root‐mean‐square for a periodic signal helps in calculation of power in a resistor. The average power in a resistor when a dc voltage Vdc is applied across a resistor would be Pavg 79 2 Vdc R EE1002 Introduction to Circuits and Systems RMS of a sinusoid Consider the sinusoidal voltage v(t ) Vm cos(t ) . The RMS value of this voltage will be T Vrms T 12 1 2 2 v (t )dt T Vm cos (t )dt T0 0 T 2 V2 V 1 Vm (1 cos 2(t ))dt m m T 2 2 2 0 The cosine function integrated over one time period will contribute zero t the integration. Usually in discussing sinusoids, the RMS value is given rather than the peak value. For example when we say the PUB supply in Singapore is 230V, we mean that the RMS value of the PUB supply is 230V and its peak value would be Vm 2Vrms 230 2 230 1.414 325V Phasors Sinusoidal voltages and currents can be represented as vectors in a complex plane. These are called Phasors and are very useful in steady‐state analysis of sinusoidal voltag...
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