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Q5Q

Expert-verifiedFound in: Page 935

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**Curve a in Fig. 31-21 gives the impedance Z of a driven RC circuit versus the driving angular frequency ${{\mathit{\omega}}}_{{\mathbf{d}}}$. The other two curves are similar but for different values of resistance R and capacitance C. Rank the three curves according to the corresponding value of R, greatest first.**

According to the value of resistance, the circuits are ranked as $Circuit\text{}c>Circuit\text{}b>\text{}Circuit\text{}a$.

- The three circuits have different resistors and capacitors.
- Curve b and curve c are similar.

**The impedance of the RC circuit is the effective resistance of an electric circuit or component to alternating current, arising from the combined effects of resistance and reactance. Thus, it depends on the resistance and the reactance of the capacitor. The reactance of the capacitor varies with the angular frequency of the oscillation.**

Formula:

The impedance of a RC circuit, ${\mathit{Z}}{\mathbf{=}}{\mathbf{}}\sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}\frac{\mathbf{1}}{{\left(\omega C\right)}^{\mathbf{2}}}}{\mathbf{}}$ (i)

** **

The analysis of the formula of equation (i) gives us the information that as $\omega $increases, the value of decreases $\frac{1}{{\left(\omega C\right)}^{2}}$. Thus, for higher values of ω, the capacitive reactance becomes less significant as compared to the resistance.

Thus, the graph of the impedance gives information about the resistance R at higher frequencies.

From the graph, we can see that at higher frequencies, the graph of circuit c has the highest resistance than circuit a and circuit b.

Hence, we rank the circuits in decreasing order of R as $Circuit\text{}c>Circuit\text{}b>\text{}Circuit\text{}a$.

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