Current Electricity

Step 1: Concept
Use the current distribution law in parallel circuits and Ohm's law ( ).
Step 2: Resistance Analysis
As and resistances are in parallel, equivalent resistance is . This and are in series, giving .
Step 3: Current Calculation
Total current . This enters the parallel combination. Using current distribution for the branch: .
Step 4: Potential Difference
$ $
Final Answer: (C)

Concept: Circuit I:
Capacitors in series: Resistors in parallel: Circuit II:
Capacitors in parallel: Resistors in series: Circuit III:
Capacitors in series: Resistors in parallel: But effective configuration doubles resistance path: Conclusion:

Step 1: Understanding the Concept:
In a parallel combination, voltage across galvanometer = voltage across shunt.
Step 2: Detailed Explanation:

.
Step 3: Final Answer:

Step 1: Understanding the Concept:
Potential gradient of a potentiometer: . It changes when the length of the wire changes (keeping same).
Step 2: Detailed Explanation:
Original length: , . Balance point initially: . New length: . New potential gradient: . Using : . Substituting: .
Step 3: Final Answer:

Step 1: Understanding the Concept:
Compare current in in two cases: with both batteries in circuit, and when is short-circuited.
Step 2: Detailed Explanation:
Current with both batteries: . Current with shorted: . Condition: . Cross multiplication: . Simplifying: .
Step 3: Final Answer:

Step 1: Initial charges: , . Net charge = .

Step 2: Equivalent capacitance = . V.

Step 1: , .

Step 2: .

Step 1: Chemical properties depend on atomic number (number of protons).

Step 2: Adding neutrons changes mass number but not atomic number, so chemical properties remain same.

Step 1: J.

Step 2: Convert to eV: eV.

Step 1: In potentiometer, null point is independent of series resistance.

Step 2: Therefore, null point remains at 240 cm.

Step 1: Understanding the Concept:
Between any two corners of the triangle, one resistor (2 ) is in parallel with two resistors in series (4 ).
Step 2: Detailed Explanation:

Step 3: Final Answer:
Resistance between any two corners .

Step 1: Understanding the Concept:
Impedance . Peak current .
Step 2: Detailed Explanation:



At resonance approximation or with calculated : A
Step 3: Final Answer:
Peak current A.

Step 1: Understanding the Concept:
Current in circuit . Voltmeter reading .
Step 2: Detailed Explanation:

Step 3: Final Answer:
Potential difference V.

Step 1: Understanding the Concept:
When no current passes through the galvanometer (Wheatstone bridge balanced): . Also apply KCL at junctions.
Step 2: Detailed Explanation:
From the circuit: Current through 10 = 3 A; through = 1 A.
Using Kirchhoff's laws and bridge balance condition with given resistances (24 , 84 , 30 , 10 , , ):
By voltage division and Wheatstone balance: , .
Step 3: Final Answer:
and .

Step 1: Understanding the Concept:
. Ratio: .
Step 2: Detailed Explanation:

Step 3: Final Answer:
Temperature coefficient C .

Step 1: Understanding the Concept:
For two identical cells (emf , internal resistance ), current in series: ; current in parallel: .
Step 2: Detailed Explanation:
Setting : So .
Step 3: Final Answer:
The internal resistance of each cell is 1.5 .

Step 1: Understanding the Concept:
Use Kirchhoff's laws to solve for currents.
Step 2: Detailed Explanation:
Applying Kirchhoff's current and voltage laws at the junctions, the current A.
Step 3: Final Answer:
The magnitude of current is A.

Step 1: Understanding the Concept:
Colour code: Black(0), Brown(1), Red(2), Orange(3), Yellow(4), Green(5), Blue(6), Violet(7), Grey(8), White(9).
Step 2: Detailed Explanation:
The colour bands are White, Brown, Red, Silver. White = 9, Brown = 1, Red = , Silver = . So resistance = .
Step 3: Final Answer:
The resistance is .

Step 1: Understanding the Concept:
Potential gradient , and .
Step 2: Detailed Explanation:
Required potential gradient mV/cm V/m. Total potential drop across wire V. Current A. Total resistance in circuit . Additional resistance .
Step 3: Final Answer:
The additional resistance required is .

Step 1: Understanding the Concept:
Motor efficiency , loss = .
Step 2: Detailed Explanation:
Input power = W. Output power = efficiency input = W. Power loss in winding = W. So .
Step 3: Final Answer:
The resistance of the winding is .

Step 1: Understanding the Concept:
Shunt resistance .
Step 2: Detailed Explanation:
mA, , A. .
Step 3: Final Answer:
The shunt required is .

Step 1: Understanding the Concept:
Phase difference = .
Step 2: Detailed Explanation:
Phase difference = . Since current phase is greater, current leads voltage by .
Step 3: Final Answer:
Current leads voltage by .

Step 1: Understanding the Concept:
In a potentiometer, the balancing length is directly proportional to the emf.
Step 2: Detailed Explanation:
and . Dividing, . Solving gives , so ratio .
Step 3: Final Answer:
The ratio is 3:1.

Step 1: Understanding the Concept:
Each part has resistance . The triangle has resistances on each side.
Step 2: Detailed Explanation:
When cell is connected across B and C, the resistances AB and AC are in series (total ) and this combination is in parallel with BC ( ). Equivalent resistance = . Current from cell = A. Current through AB = current through AB-AC branch = A (since current divides in ratio of resistances). Potential difference across AB = V.
Step 3: Final Answer:
The potential difference across AB is 1V.

Step 1: Understanding the Concept:
Simplify using series and parallel combinations.
Step 2: Detailed Explanation:
and parallel:
and parallel:
and series:
and parallel:
Step 3: Final Answer:
Equivalent resistance is .

Step 1: Understanding the Concept:
Energy .
Step 2: Detailed Explanation:

Step 3: Final Answer:
Energy is 432 kJ.

Step 1: Understanding the Concept:
Power , minimum R gives max power.
Step 2: Detailed Explanation:
Let each
A: ,
B: ,
C: ,
D: ,
A gives highest power.
Step 3: Final Answer:
Circuit A dissipates greatest power.

Step 1: Understanding the Concept:
.
Step 2: Detailed Explanation:




Step 3: Final Answer:
Temperature is 1100 K.