Basic Electronics, Chapter 3: Challenge 1 solution (decode, encode and power)

(a) Decoding. Digit bands first, then the multiplier, then tolerance.

  brown-black-orange-gold
    1, 0, x 1 k, gold = 5 %          ->  10 k ohm +/-5 %
    range: 10,000 x 0.95 = 9,500 ohm  to  10,000 x 1.05 = 10,500 ohm

  yellow-violet-red-gold
    4, 7, x 100, gold = 5 %          ->  4.7 k ohm +/-5 %
    range: 4,700 x 0.95 = 4,465 ohm  to  4,700 x 1.05 = 4,935 ohm

  green-blue-brown-brown   (4-band: brown tolerance = 1 %)
    5, 6, x 10, brown = 1 %          ->  560 ohm +/-1 %
    range: 560 x 0.99 = 554.4 ohm  to  560 x 1.01 = 565.6 ohm

  red-red-black-red-brown   (5-band: three digits, multiplier, tolerance)
    2, 2, 0, x 100, brown = 1 %      ->  220 x 100 = 22,000 ohm = 22 k ohm +/-1 %
    range: 22,000 x 0.99 = 21,780 ohm  to  22,000 x 1.01 = 22,220 ohm

(b) Encoding.

  330 ohm, 5 %  = 33 x 10        -> orange, orange, brown, gold
  6.8 k, 5 %    = 68 x 100       -> blue, grey, red, gold
  100 k, 1 %    (5-band) = 100 x 1 k   -> brown, black, black, orange, brown
                  (digits 1,0,0 then multiplier orange = x 1 k, then brown = 1 %)

(c) Derating a 1/4 W resistor at 100 C.
  P_allowed = P_rated x (155 - T) / (155 - 70)
            = 0.25 x (155 - 100) / 85
            = 0.25 x 55 / 85
            = 0.1618 W
  The actual 0.15 W is below 0.162 W, so it is within the limit, but it is
  0.15 / 0.1618 = 93 % of the derated limit: far too little margin.
  A 1/2 W part would allow 0.5 x 55 / 85 = 0.3235 W, so 0.15 W would be 46 %.
  Better choice: the 1/2 W resistor.

(d) 12 V across 470 ohm.
  P = V^2 / R = 144 / 470 = 0.3064 W
  Current check: I = 12 / 470 = 25.5 mA;  P = I^2 R = 0.0255^2 x 470 = 0.306 W. Same.
  Rule: P must be at most 50 % of the rating, so rating >= 0.3064 / 0.5 = 0.613 W.
    1/4 W (0.25 W):  P is 123 % of the rating  -> fails
    1/2 W (0.5 W):   P is 61 % of the rating   -> fails the 50 % rule
    1 W:             P is 31 % of the rating   -> passes
  Answer: use a 1 W resistor (or reduce the voltage or increase the resistance).

Checklist
 [ ] read from the end nearest a band edge, digits then multiplier then tolerance
 [ ] 4-band: 2 digits; 5-band: 3 digits
 [ ] tolerance range = value x (1 +/- tolerance)
 [ ] P = V^2/R; choose a rating of at least twice the power
 [ ] derate for temperature above 70 C