Wave Particle Duality and Quantum Physics

Question

If you plug in a 100W bulb and a 40W bulb, which bulb will appear brighter? 

If you plug in a 100W bulb and a 40W bulb, which bulb will feel hotter?

explain using physics please

Answer 1

(a)

Let us consider 40 w and 100 w bulbs are connected in series .

Assume the supply voltage v = 120 .

Resistance at 40 w bulb is = (voltage)² / power  ⇒ (120)² / 40 = 360 ohm .

Resistance at 100 w bulb is  ⇒(voltage)² / power  ⇒ (120)² / 100 = 144 ohm .

So the total resistance in the circuit is 360 + 144 = 504 ohm .

The total current in the circuit  I = voltage / resistance ⇒ 120 / 504 = 0.2380 A .

The voltage drop across 40 w bulb is = Total circuit current * resistance at 40 w bulb

                                                          = 0.2380 * 360 = 85.714 V .

The voltage drop across 100 w bulb is = Total circuit current * resistance at 100 w bulb

                                                           = 0.2380 * 144 = 34.285  V .

The power consumed at 40 w bulb = voltage drop at 40 w * circuit current 

                                                      ⇒ 85.714 * 0.2380 = 20.399 w .

The power consumed at 100 w bulb = voltage drop at 100 w * circuit current

                                                        ⇒ 34.285* 0.2380 = 8.16 w .

So 40 w bulb burns more than 100 w bulb this means 40 w bulb is brighter .

Check :

Total voltage in the circuit is sum of the individual voltage drops at 40 w and 100 w . [Kirchoff's law ]

120 = 85.714 + 34.285 .

Answer 2

(b)

Amount of power consumed by 40 w bulb is 20.399 w . [From (a)]

Amount of power consumed by 100 w bulb is 8.16 w . 

The bulb which consumes more power will feel more hotter .

Hence 40 w bulb will feel hotter .