- 1(current)
Q. No.Given below are two statements:
| Statement I: | A \(\mathrm{Li}\text{-ion}\) battery stores electric charge as well as electrical energy. |
| Statement II: | A charged capacitor stores electrical energy. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Grouping of Cells |
Level 4: Below 35%
Hints
Two non-ideal batteries are connected in parallel: Battery of EMF \(E_1,\) resistance \(r_1\) and of EMF \(E_2,\) resistance \(r_2.\) The resulting equivalent battery has EMF '\(E,\)' resistance \(r.\) If \(r_1<r_2,\)
| 1. | \(|E-E_1|<|E-E_2|\) | 2. | \(|E+E_1|<|E+E_2|\) |
| 3. | \(|E-E_1|>|E-E_2|\) | 4. | \(|E+E_1|>|E+E_2|\) |
Subtopic: Grouping of Cells |
Level 3: 35%-60%
Hints
Two cells having emfs \(3\) V and \(2\) V are connected in parallel and they give an emf of \(0.5\) V in the same sense as \(3\) V \(-\) cell. The internal resistances of the cells are \(r_1\) and \(r_2\) respectively. If one cell is reversed, their combined emf becomes \(2.5\) V. The ratio of their internal resistances \(\Big(\dfrac{r_1}{r_2}\Big) \) is:
1. \(1\)
2. \(\dfrac12\)
3. \(\dfrac21\)
4. \(\sqrt2\)
1. \(1\)
2. \(\dfrac12\)
3. \(\dfrac21\)
4. \(\sqrt2\)
Subtopic: Grouping of Cells |
67%
Level 2: 60%+
Hints
The maximum power that a combination of two cells of EMF \(E_1\) & \(E_2\) \((E_1>E_2)\) can transfer to an external resistance is \(2~\text{W},\) when they are connected in series. When the EMF's are connected in opposite sense, but in series, this power is \(0.5~\text{W}.\) The ratio of the EMF's is, \((E_1/E_2)\)
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
Subtopic: Grouping of Cells |
61%
Level 2: 60%+
Hints
In Column-I are quantities associated with some devices, and in Column-II are the rules for finding equivalent values when these devices are connected in certain manner. For each quantity in Column-I, match the correct law of combination in Column-II.
| Column-I | Column-II | ||
| (A) | EMF's of ideal cells \((X)\) in the same orientation | (I) | In series, \(X_{\text{eq}}=X_1+X_2+...\) |
| (B) | Resistances \((X)\) | (II) | In parallel, \(\dfrac{1}{X_{\text{eq}}}=\dfrac{1}{X_1}+\dfrac{1}{X_2}+...\) |
| (C) | Capacitances \((X)\) | (III) | In series, \(\dfrac{1}{X_{\text{eq}}}=\dfrac{1}{X_1}+\dfrac{1}{X_2}+...\) |
| (D) | Conductances \((X)\) | (IV) | In parallel, \(X_{\text{eq}}=X_1+X_2+...\) |
| 1. | \(\mathrm{A\text-I,II;B\text-I,II;C\text-III,IV;D\text-III,IV}\) |
| 2. | \(\mathrm{A\text-I,II;B\text-I,II;C\text-III,IV;D\text-I,II}\) |
| 3. | \(\mathrm{A\text-I;B\text-I,II;C\text-III,IV;D\text-III,IV}\) |
| 4. | \(\mathrm{A\text-I;B\text-I,II;C\text-III,IV;D\text-I,II}\) |
Subtopic: Grouping of Cells |
Level 3: 35%-60%
Hints
All the cells shown in the combinations are identical, having an EMF of \(6~\text V\) and internal resistance of \(1~\Omega.\) In Column-I, are shown some combinations of cells with the final connecting terminals as \(A\) & \(B.\) In Column-II, are mentioned the EMF's of these combinations \((E) \) & the maximum currents that can be drawn \(\left(I_{\text{max}}\right).\) Match the correct combination in Column-I with their corresponding values in Column-II. Note that the internal resistances are not shown.
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) |  |
\(\mathrm{(I)}\) | \(E=0~\text V,I_{\text{max}}=0~\text A\) |
| \(\mathrm{(B)}\) |  |
\(\mathrm{(II)}\) | \(E=6~\text V,I_{\text{max}}=8~\text A\) |
| \(\mathrm{(C)}\) |  |
\(\mathrm{(III)}\) | \(E=4~\text V,I_{\text{max}}=6~\text A\) |
| \(\mathrm{(D)}\) |  |
\(\mathrm{(IV)}\) | \(E=2.4~\text V,I_{\text{max}}=6~\text A\) |
| 1. | \(\mathrm{A\text-IV,B\text-IV,C\text-I,D\text-I}\) |
| 2. | \(\mathrm{A\text-III,B\text-I,C\text-I,D\text-I}\) |
| 3. | \(\mathrm{A\text-II,B\text-I,C\text-III,D\text-I}\) |
| 4. | \(\mathrm{A\text-II,B\text-III,C\text-IV,D\text-I}\) |
Subtopic: Grouping of Cells |
Level 3: 35%-60%
Hints
When ideal cells with EMF's \(E_1,E_2\) and initially uncharged capacitors \(C_1,C_2\) are connected in parallel, the system can be replaced by a single cell of EMF \(E_{\text{eq}}\) and capacitance \(C_{\text{eq}}\) – just as we do it for parallel combination of cells with internal resistances.
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
The potential difference between \(A\) & \(B\) will be:
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
The potential difference between \(A\) & \(B\) will be:
| 1. | \(3.5~\text V\) | 2. | \(1.5~\text V\) |
| 3. | \(4~\text V\) | 4. | \(7~\text V\) |
Subtopic: Grouping of Cells |
70%
Level 2: 60%+
Hints
When ideal cells with EMF's \(E_1,E_2\) and initially uncharged capacitors \(C_1,C_2\) are connected in parallel, the system can be replaced by a single cell of EMF \(E_{\text{eq}}\) and capacitance \(C_{\text{eq}}\) – just as we do it for parallel combination of cells with internal resistances.
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
The potential differences across the \(4~\mu \text F\) and \(2~\mu \text F\) capacitors will have the magnitudes, respectively:
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
The potential differences across the \(4~\mu \text F\) and \(2~\mu \text F\) capacitors will have the magnitudes, respectively:
| 1. | \(1~\text V,2~\text V\) | 2. | \(1.5~\text V,1.5~\text V\) |
| 3. | \(3.5~\text V,0.5~\text V\) | 4. | \(2~\text V,5~\text V\) |
Subtopic: Grouping of Cells |
Level 3: 35%-60%
Hints
When ideal cells with EMF's \(E_1,E_2\) and initially uncharged capacitors \(C_1,C_2\) are connected in parallel, the system can be replaced by a single cell of EMF \(E_{\text{eq}}\) and capacitance \(C_{\text{eq}}\) – just as we do it for parallel combination of cells with internal resistances.
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
If an external resistance of \(2~\Omega\) is connected between \(A\) & \(B,\) the current that would flow through it is, initially:
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
If an external resistance of \(2~\Omega\) is connected between \(A\) & \(B,\) the current that would flow through it is, initially:
| 1. | \(2.5~\text A\) | 2. | \(1~\text A\) |
| 3. | \(3.5~\text A\) | 4. | \(2~\text A\) |
Subtopic: Grouping of Cells |
59%
Level 3: 35%-60%
Hints
When ideal cells with EMF's \(E_1,E_2\) and initially uncharged capacitors \(C_1,C_2\) are connected in parallel, the system can be replaced by a single cell of EMF \(E_{\text{eq}}\) and capacitance \(C_{\text{eq}}\) – just as we do it for parallel combination of cells with internal resistances.
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
If the \(2~\text V\) cell is reversed and an external resistance of \(2~\Omega\) is connected between \(A\) & \(B,\) the initial current through the \(2~\Omega\) resistance will be:
The replacement rule is shown here for two capacitors (and the cells):
\(E_{\text{eq}}=\dfrac{C_1E_1+C_2E_2}{C_1+C_2}\) & \(C_{\text{eq}}=C_1+C_2\)
Note that one needs to keep in mind the direction of the EMF.
Two cells of EMFs \(5~\text V\) & \(2~\text V\) are connected with \(4~\mu \text F\) & \(2~\mu \text F\) capacitors:
The two capacitors are initially uncharged.
If the \(2~\text V\) cell is reversed and an external resistance of \(2~\Omega\) is connected between \(A\) & \(B,\) the initial current through the \(2~\Omega\) resistance will be:
| 1. | \(\dfrac43~\text A\) | 2. | \(\dfrac83~\text A\) |
| 3. | \(\dfrac32~\text A\) | 4. | \(\dfrac74~\text A\) |
Subtopic: Grouping of Cells |
62%
Level 2: 60%+
Hints
- 1(current)
Q. No.
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