Question

(a) Two bulbs rated 25W – 220V and 100W – 220V are connected in series to a 440V supply. Show with necessary calculations which bulb, if any, will fuse? 

(b) What should happen if the two bulbs were connected in parallel to the same supply?

Answer 1

Let i₁, i₂ be the maximum allowed current in the two bulbs and R₁ and R₂ be their respective resistances.

∴ R₁ = \(\frac{(220)^2}{25}\) 

= 1936 Ω 

i₁ = \(\frac{P_1}{V}\) 

= \(\frac{25}{220}\) = 0.114 A

R₂ = \(\frac{(220)^2}{25}\) 

= 484 Ω

i₂ = \(\frac{P_2}{V}\) 

= \(\frac{100}{220}\) 

= 0.454A 

(a) When bulbs are connected in series, net resistance

R_s = R₁ + R₂ 

= 1936 + 484 

= 2420 Ω

∴ Current in the circuit,

i = \(\frac{V'}{R_s}\) 

= \(\frac{440}{2420}\) 

= 0.18A 

Since, 

i > i₁ 

But,

 i < i₂, 

Therefore, 

25 W bulb will fuse.

(b) When bulbs are connected in parallel, let the currents through bulb I and II be i₁' and i₂'. In parallel combination, the voltage across each bulb is the same.

∴i₁' = \(\frac{440}{R_1}\)

= \(\frac{440}{1936}\) 

= 0.23A 

 i₂' = \(\frac{440}{484}\) 

= 0.91A 

As i₁' > i₁ and i₂' > i₂, 

Hence both the bulbs will fuse.