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. \(\large\frac{t_1t_2}{t_1+t_2}\)
2. \(t_1+t_2\)
3. \({\large\frac12}(t_1+t_2)\)
4. \(\large\frac{t_1t_2}{2(t_1+t_2)}\)
Subtopic: Heating Effects of Current |
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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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A wire of length \('l'\) and resistance \(100 ~\Omega\) is divided into \(10\) equal parts. The first \(5\) parts are connected in series while the next \(5\) parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
1. \(52~ \Omega\)
2. \(55~ \Omega\)
3. \(60 ~\Omega\)
4. \(26~ \Omega\)
Subtopic: Combination of Resistors |
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The terminal voltage of the battery, whose emf is \(10~\text V\) and internal resistance \(1~\Omega,\) when connected through an external resistance of \(4~\Omega\) as shown in the figure is:
1. \(6~\text V\)
2. \(8~\text V\)
3. \(10~\text V\)
4. \(4~\text V\)
Subtopic: EMF & Terminal Voltage |
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A uniform wire of diameter \(d\) carries a current of \(100~\text{mA}\) when the mean drift velocity of electrons in the wire is \(v.\) For a wire of diameter \({\frac{\mathrm{d}}{2}}\) of the same material to carry a current of \(200~\text{mA},\) the mean drift velocity of electrons in the wire is:
1. \(4v\)
2. \(8v\)
3. \(v\)
4. \(2v\)
Subtopic: Current & Current Density |
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In an electrical circuit, the voltage is measured as \({V}=(200\pm4)\) volts and the current is measured as \({I}=(20\pm0.2)~\text A.\) The value of the resistance is:
1. \((10\pm4.2)~\Omega \)
2. \((10\pm0.3)~\Omega \)
3. \((10\pm0.1)~\Omega \)
4. \((10\pm0.8)~\Omega \)
Subtopic: Derivation of Ohm's Law |
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