Series Connected Bulbs – Rankers Physics

Power of Electrical Circuit: Practice Problem & Solution

Assertion (A): \(100 \text{ W}\), \(60 \text{ W}\) and \(20 \text{ W}\) bulbs, each marked \(220 \text{ volt}\), are connected in series with a voltage source, then \(20 text{ W}\) bulb gives maximum illumination. Reason (R): Resistance of filament \(20 \text{ W}\) bulb is maximum.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Power of Electrical Circuit. Understanding the underlying formula is key to arriving at the correct answer below:

The power rating of a bulb is given by \(P = V^2 / R\). For bulbs rated at the same voltage \(V\) (here \(220 text{ V}\), resistance \(R = V^2 / P\). A lower power rating implies higher resistance. Thus, the \(20 \text{ W}\) bulb has the highest resistance (Reason R is true). When bulbs are connected in series, the same current \(I\) flows through each. The power dissipated by each bulb is \(P_{actual} = I^2 R\). Since \(I\) is common, the bulb with the highest resistance will dissipate the most power and therefore glow brightest. Hence, the \(20 \text{ W}\) bulb will provide maximum illumination (Assertion A is true). Reason (R) correctly explains Assertion (A).

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): In \(R = R_0(1 + \alpha\Delta T)\) when temp. is increased from \(27^\circ C\) to \(227^\circ C\) resistance increases from \(100 \Omega\) to \(150 \Omega\) this implies \(\alpha = 2.5 \times 10^{-3} /^{\circ} C\). Reason (R): (R = R_0(1 + \alpha\Delta T)\) is valid only when change in temp \(\Delta T\) is very small i.e. \(\Delta R = (R-R_0) \ll R_0\).
2. Consider the following statements: (A) The electromotive force (EMF) of a cell is equal to the potential difference across its terminals when no current is flowing. (B) Voltage drop happens in a cell due to internal resistance when current flows through it. (C) If multiple identical cells are connected in series, the total EMF decreases. (D) If multiple identical cells are connected in parallel with their positive terminals on the same side, the total EMF remains same as individual cell. Which of the above statement(s) is/are correct?
3. Assertion (A): A voltmeter is an inherently inaccurate instrument. Reason (R): A voltmeter is always connected in parallel in a circuit.  
4. There are 45 number of cells with internal resistance of each cell is 0.5Ω To get the maximum current through a resistance of 2.5Ω, one can use m rows of cells, each row having n cells. The values of m and n are:
5. A wire $50\text{ cm}$ long and $1\text{ mm}^2$ in cross-section carries a current of $4\text{ A}$ when connected to a $2\text{ V}$ battery. The resistivity of the wire is: (1994)