Question

In a domestic circuit five LED bulbs are arranged as shown. The source voltage is 220 V and the power rating of each bulb is marked in the circuit diagram. Based on the following circuit diagram, answer the following questions:

(a) State what happens when
(i) key K₁ is closed.
(ii) key K₂ is closed.
(b) Find the current drawn by the bulb B when it glows.
(c) Calculate
(i) the resistance of bulb B, and
(ii) total resistance of the combination of four bulbs B, C, D and E.
OR
(c) What would happen to the glow of all the bulbs in the circuit when keys K₁ and K₂ both are closed and the bulb C suddenly get fused ? Give reason to justify your answer.

Answer 1

(i) When \(K_1\) is closed:
  The circuit becomes complete for the single bulb marked 22 W, 220 V.
    The power rating of the bulb indicates it is designed to work at 220 V.
    The current flowing through the bulb can be calculated using the formula for power:
   \[P = V \cdot I \quad \Rightarrow \quad I = \frac{P}{V}\]
   Substituting the values:
   \[I = \frac{22}{220} = 0.1 \, \text{A}\]
    Thus, a current of 0.1 A flows through the 22 W bulb, which glows normally.
    The other four bulbs remain \textbf{OFF} because \(K_2\) is open, making their circuit incomplete.
(ii) When \(K_2\) is closed:
   Now, the four bulbs rated 11 W, 55 V each are connected in series.
   In a series circuit, the voltage divides equally among all components when they have the same rating.
   Total source voltage = 220 V, number of bulbs = 4, so the voltage across each bulb is:
 

\[V_{each bulb} = \frac{220V}{4} = 55 \, V\]

    Since each bulb operates at its rated voltage of 55 V, they all glow normally.
    To verify the current flowing through the series circuit, we use the formula for power:
   \[P = V \cdot I \quad \Rightarrow \quad I = \frac{P}{V}\]
   For one bulb:
   \[I = \frac{11}{55} = 0.2 \, A\]
    In a series circuit, the same current flows through all bulbs. Thus, a current of 0.2 A flows through the entire series circuit.
Summary of observations:
   When \(K_1\) is closed: The 22 W bulb glows normally with a current of 0.1 A. The 11 W bulbs remain off as their circuit is incomplete.
   When \(K_2\) is closed: The four 11 W bulbs glow normally, with 55 V across each bulb and a total current of 0.2 A flowing through the series circuit.