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Q. No.A wire is connected to form an equilateral triangle \(ABC\), each side having a resistance of \(4~\Omega\). The vertex \(C\) is maintained at zero volts (\(V_C=0\)), and currents flowing in at \(A\) and \(B\) are as shown in the figure. The ratio of the potentials at \(D\) and \(E\) \(\Big(i.e.~\frac{V_D}{V_E}\Big)\) equals:
1.
\(\dfrac31\)
2.
\(\dfrac21\)
3.
\(\dfrac11\)
4.
\(\dfrac53\)
Subtopic: Â Kirchoff's Current Law |
Level 3: 35%-60%
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\(AB\) is a \(20~\Omega\) resistor with a tapping point \(C\) that can be moved along \(AB\). The resistances in \(AC,BC\) are proportional to the lengths \(AC,BC\). Initially, \(C\) is at the mid-point of \(AB\) and the circuit is switched on.
If the tapping point \(C\) is moved so that the length \(BC\) is reduced to half its initial value, then the voltage across the \(15~\Omega\) resistor,
If the tapping point \(C\) is moved so that the length \(BC\) is reduced to half its initial value, then the voltage across the \(15~\Omega\) resistor,
| 1. | increases by \(1\) V |
| 2. | decreases by \(1\) V |
| 3. | increases by \(3\) V |
| 4. | decreases by \(3\) V |
Subtopic: Â Kirchoff's Voltage Law |
Level 3: 35%-60%
Hints
In a Wheatstone Bridge arrangement, as shown in the figure, the bridge is balanced. However, when the resistances in the arms \(P,Q\) are switched, the bridge is balanced only when \(R\) is replaced by \(4R\) in the other two arms. If the value of \(R\) is \(100\) \(\Omega\), that of \(S\) is:
| 1. | \(100~\Omega\) | 2. | \(50~\Omega\) |
| 3. | \(200~\Omega\) | 4. | \(400~\Omega\) |
Subtopic: Â Wheatstone Bridge |
 56%
Level 3: 35%-60%
Hints
A uniformly increasing current flows through a \(30\) \(\Omega\) resistance, as shown in the graph.
The thermal energy generated in the resistance due to Joule heating is:
1. \(240\) J
2. \(480\) J
3. \(160\) J
4. \(320\) J
The thermal energy generated in the resistance due to Joule heating is:
1. \(240\) J
2. \(480\) J
3. \(160\) J
4. \(320\) J
Subtopic: Â Heating Effects of Current |
Level 4: Below 35%
Hints
All the cells, shown in the figure below, are of \(2~\text V,\) and all the resistances are \(1~\Omega.\) When a potential difference \(V\) is applied between \(A\) and \(B,\) the current through the circuit doubles compared to the situation when the potential difference is made zero. Then;
| 1. | \(V=2\) volts, positive at \(A.\) |
| 2. | \(V=2\) volts, negative at \(A.\) |
| 3. | \(V=6\) volts, positive at \(A.\) |
| 4. | \(V=6\) volts, negative at \(A.\) |
Subtopic: Â Kirchoff's Voltage Law |
Level 3: 35%-60%
Hints
All the resistances in the circuit shown below are \(2~\Omega.\) The equivalent resistance between \(A\) and \(C\) is:
| 1. | \(4~\Omega\) | 2. | \(2~\Omega\) |
| 3. | \(\dfrac43~\Omega\) | 4. | \(\dfrac{10}3~\Omega\) |
Subtopic: Â Combination of Resistors |
 73%
Level 2: 60%+
Hints
The current flowing through the left \(20~\Omega\) resistor is:
| 1. | \(1~\text A\) | 2. | \(0.5~\text A\) |
| 3. | \(2.5~\text A\) | 4. | \(3~\text A\) |
Subtopic: Â Kirchoff's Voltage Law |
 59%
Level 3: 35%-60%
Hints
When no current is passed through a conductor,
| (a) | the free electrons do not move. |
| (b) | the average speed of a free electron over a large period of time is zero. |
| (c) | the average velocity of a free electron over a large period of time is zero. |
| (d) | the average of the velocities of all the free electrons at an instant is zero. |
Choose the correct option:
| 1. | (a) only | 2. | (b), (c) |
| 3. | (c), (d) | 4. | (a), (d) |
Subtopic: Â Current & Current Density |
 56%
Level 3: 35%-60%
Hints
Links
As the temperature of a metallic resistor is increased, the product of its resistivity and conductivity:
1. increases
2. decreases
3. remains constant
4. may increase or decrease
Subtopic: Â Derivation of Ohm's Law |
 75%
Level 2: 60%+
Hints
Links
In the Wheatstone Bridge arrangement shown, the resistance \(P\) is \(2~ \Omega.\) The bridge is initially balanced. If P and Q are interchanged: an amount equal to \(S\) has to be added to \(R\) to restore the balance. The resistance \(Q\) equals (nearly):
1. \(2 ~\Omega\)
2. \(3.2 ~\Omega\)
3. \(4 ~\Omega\)
4. \(6.4 ~\Omega\)
1. \(2 ~\Omega\)
2. \(3.2 ~\Omega\)
3. \(4 ~\Omega\)
4. \(6.4 ~\Omega\)
Subtopic: Â Wheatstone Bridge |
Level 3: 35%-60%
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