Three Simple Circuits — Question 1

Question 1

A resistor power limit constrains rms voltage and sinusoidal peak separately

An ideal 150-ohm resistor may dissipate at most 3.00 W on average. It is driven by a pure sinusoidal voltage. Treat the stated limit as an average thermal limit only.

1. Find the largest rms and peak voltages allowed by that limit.

2. Find peak current and peak instantaneous power at that operating point.

Question 1 - Solution

A resistor power limit constrains rms voltage and sinusoidal peak separately

(a) Method and calculation

$$P_{\mathrm{avg}}=V_{\mathrm{rms}}^2/R\Rightarrow\boxed{V_{\mathrm{rms}}=\sqrt{(3)(150)}=21.2132\,V}.$$$$\boxed{V_p=\sqrt2V_{\mathrm{rms}}=30.0\,V}.$$

(b) Interpretation and further calculation

$$I_p=V_p/R=30/150=.200\,A.$$$$\boxed{p_{\max}=V_pI_p=6.00\,W=2P_{\mathrm{avg}}}.$$

Physical check

The sinusoidal peak dissipation is twice its cycle average; an average rating alone does not specify separate pulse limits.