An L-R-C series circuit has L = 0.450 H, C = 2.50 * 10^-5 F, and resistance R. (b) What value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in part (a)?
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1
Calculate the natural angular frequency () for the L-R-C circuit using the formula , where L is the inductance and C is the capacitance.
Determine the decreased angular frequency () which is 5% less than the natural angular frequency. Use the relation .
Use the formula for the angular frequency of a damped L-R-C circuit, , and set to find the relationship involving R.
Solve the equation for R. Rearrange to get .
Substitute the values of L, , and into the equation to find the required value of R.