An ac generator generating an emf is connected to a resistor. Draw a labelled graph of current (I)…
Physics20275 marksNumerical
An ac generator generating an emf $e = 300 \sin(100\pi t)\text{V}$ is connected to a $100\,\Omega$ resistor.
(a)[1.25]
Draw a labelled graph of current (I) flowing through it versus time (t). Draw one cycle only.
(b)[1.25]
Calculate the average power consumed by the resistor.
(c)[1.25]
Why ac is preferred to dc, though it has varying values whereas the latter has a fixed value?
(d)[1.25]
State any one difference between a transformer used at the power generating station and the transformer in a city which is used to supply power to households.
Answer
Answer (a)
AI
Peak current $i_0 = \frac{e_0}{R} = \frac{300}{100} = 3\cdot0\text{ A}$. Angular frequency $\omega = 2\pi f = 100\pi \implies f = 50\text{ Hz}$, period $T = 1/50 = 0\cdot02\text{ s} = 20\text{ ms}$. The waveform is a standard sine wave of amplitude $3\text{ A}$ and time period $0\cdot02\text{ s}$.
Answer (b)
AI
Average power $\langle P \rangle = \frac{I_0^2 R}{2} = \frac{3^2 \times 100}{2} = \frac{900}{2} = 450\text{ W}$.
Final answer: 450 W
Answer (c)
AI
AC is preferred over DC for long-distance power transmission because AC voltages can be stepped up or down efficiently using transformers, which minimizes power loss ($I^2R$) during transmission.
Answer (d)
AI
The transformer at a power generating station is a step-up transformer (to transmit power at high voltage and low current), whereas the transformer in a city supplying households is a step-down transformer (to lower voltage to safe levels like 220V).
