DP 4-3 A wiring circuit for a special lamp in a home is shown in Figure DP 4-3. The lamp has a resistance of 2 Ω, and the designer selects R = 100 Ω. The lamp will light when I ≥ 50 mA but will burn out when I > 75 mA.

(a) Determine the current in the lamp and determine if it will light for R = 100 Ω.

(b) Select R so that the lamp will light but will not burn out if R changes by ± 10 percent because of temperature changes in the home.

Figure DP 4-3

Do mesh analysis, right mesh is i and left mesh I will call i_L

Use second equation to solve i_L

Now plug this into other equation

(a) Determine the current in the lamp and determine if it will light for R = 100 Ω.

Lamp Will Not Light!!!

(b) Select R so that the lamp will light but will not burn out if R changes by ± 10 percent because of temperature changes in the home.

From our equation

If R increases by 10 %, i will decrease, so the larger R is the smaller current is so we must have

If R decreases by 10 % i will increase so that the smaller R is the larger current so we must have

Solve each to find upper and lower limits on R

So Range on R is

Choose R = 25 Ω,

Lamp would light !!

+ 10%

Lamp Still Lit!!

-10%

Lamp Still good!

One Choice would be 25 Ω

Many other choices exist!

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This page last updated on February 7, 2019