Two heaters \(\mathrm{A}\) and \(\mathrm{B}\) have power rating of \(1~\text{kW}\) and \(2~\text{kW}\), respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:
1. \(2:9\)
2. \(1:2\)
3. \(2:3\)
4. \(1:1\)
Subtopic:  Heating Effects of Current |
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There are two heaters \(A\) and \(B.\) Heater \(A\) takes time \(t_1\) to boil a given quantity of water, while \(B\) takes time \(t_2\) to boil the same quantity of water across same supply voltage. If the two heaters are connected in series, time taken by this combination to boil the same quantity of water will be:
1. \(\large\dfrac{t_1t_2}{t_1+t_2}\) 2. \(t_1+t_2\)
3. \({\large\dfrac12}(t_1+t_2)\) 4. \(\large\dfrac{t_1t_2}{2(t_1+t_2)}\)
Subtopic:  Heating Effects of Current |
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Two resistors of resistance, \(100\) \(\Omega\) and \(200\) \(\Omega\) are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in \(100\) \(\Omega\) resistor to that in \(200\) \(\Omega\) resistor in a given time is:
1. \(4:1\)
2. \(1:2\)
3. \(2:1\)
4. \(1:4\)
Subtopic:  Heating Effects of Current |
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Which of the following acts as a circuit protection device?

1. Fuse 2. Conductor
3. Inductor 4. Switch
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Six similar bulbs are connected as shown in the figure with a DC source of emf \(E\) and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section \(\mathrm{A}\) and one from section \(\mathrm{B}\) are glowing, will be:

      

1. \(2:1\) 2. \(4:9\)
3. \(9:4\) 4. \(1:2\)
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A filament bulb (\(500\) W, \(100\) V) is to be used in a \(230\) V main supply. When a resistance\(R\) is connected in series, the bulb works perfectly and consumes \(500\) W. The value of \(R\) is:

1. \(230\) Ω 2. \(46\) Ω
3. \(26\) Ω 4. \(13\) Ω
Subtopic:  Heating Effects of Current |
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The charge flowing through a resistance \(R\) varies with time \(t\) as \(Q=at-bt^2,\) where \(a\) and \(b\) are positive constants. The total heat produced in \(R\) is:
1. \(\dfrac{a^3R}{3b}\) 2. \(\dfrac{a^3R}{2b}\)
3. \(\dfrac{a^3R}{b}\) 4. \(\dfrac{a^3R}{6b}\)
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Two cities are \(150~\text{km}\) apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is \(8\) volts and the average resistance per km is \(0.5~\text{ohm}\). The power loss in the wire is:
1. \(19.2~\text{W}\)
2. \(19.2~\text{kW}\)
3. \(19.2~\text{J}\)
4. \(12.2~\text{kW}\)

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If the voltage across a bulb rated \((220~\text{V}\text-100~\text{W})\) drops by \(2.5\%\) of its rated value, the percentage of the rated value by which the power would decrease is:
1. \(20\%\)
2. \(2.5\%\)
3. \(5\%\)
4. \(10\%\)

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The power dissipated in the circuit shown in the figure is \(30~\text{Watts}\). The value of \(R\) is:
    
1. \(15~\Omega\)
2. \(10~\Omega\)
3. \(30~\Omega\)
4. \(20~\Omega\)

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