Calculating the Current in a Single-Loop Circuit — Question 10

Question 10

Distributing voltage over identical series resistors imposes an integer design constraint

An ideal 120 V source drives N identical 1.00 kilohm resistors in series. Each must dissipate at most .250 W and have at most 30.0 V across it. N is a positive integer.

1. Find the smallest allowed N satisfying both restrictions.

2. Find current and total dissipation for that N, and compare the individual resistor voltage and power with their limits.

Question 10 - Solution

Distributing voltage over identical series resistors imposes an integer design constraint

(a) Method and calculation

$$V_R=120/N\Rightarrow N\ge4.$$$$P_R=\frac{120^2}{N^2(1000)}\le.250\Rightarrow N\ge\sqrt{57.6}\Rightarrow N_{\min}=8.$$

(b) Interpretation and further calculation

$$I=120/(8\cdot1000)=.0150\,\mathrm A,\quad P_{\mathrm{total}}=EI=1.80\,\mathrm W.$$$$V_R=15.0\,\mathrm V,\quad P_R=I^2(1000)=.225\,\mathrm W.$$

Physical check

The power requirement is stricter here; rounding the continuous bound downward would violate a rating.