Electricity

The total resistance of the circuit when is connected to the cell is , where is the internal resistance of the cell. From Ohm's law, the current is given by: When the resistance is replaced by , the new current is: Now, solving the above two equations for , we get: Thus, the internal resistance of the cell is .

When two conductors are connected in series, the effective conductivity is given by , which is similar to the formula for resistances in parallel. Thus, the correct answer is option (2).

Using the principles of a balanced Wheatstone bridge, the ratio of the resistances leads to the determination of the voltage value, which comes out to be 2 V. Thus, the correct answer is option (4).

Step 1: Apply Parallel EMF Formula For two cells connected in parallel, the equivalent emf is given by: where: , , , . Step 2: Compute Equivalent EMF Thus, the correct answer is V. \bigskip

• Equivalent Capacitance in Series: For capacitors in series, the equivalent capacitance C_eq is given by 1/C_eq = 1/C₁ + 1/C₂. Here, C₁ = 4 μF, C₂ = 6 μF.
  1/C_eq = 1/4 + 1/6 = (3 + 2)/12 = 5/12, so C_eq = 12/5 = 2.4 μF.
• Charge Stored: The total charge Q on the equivalent capacitor is Q = C_eq × V = 2.4 × 300 = 720 μC.
• Voltage Across Each Capacitor: In series, the charge is the same across both capacitors. Voltage across a capacitor is V = Q/C.
  • For 4 μF: V₁ = Q/C₁ = 720/4 = 180 V.
  • For 6 μF: V₂ = Q/C₂ = 720/6 = 120 V.
• Verify Total Voltage: V₁ + V₂ = 180 + 120 = 300 V, which matches the applied voltage.
• Conclusion: The potential difference across the 4 μF capacitor is (3) 180 V.

Solution: To determine the power dissipated in the resistor, we will use the formula for electrical power: , where is the power in watts, is the voltage across the resistor in volts, and is the resistance in ohms.

Given:

Substitute the given values into the formula:

Therefore, the power dissipated in the resistor is 14.4 W.

To determine the power consumed by an electrical device, we use the formula for electric power:

where:

Given values are:

Substitute these values into the power formula:

Thus, the power consumed by the device is 440 W.

Step 1: Use the power-voltage-resistance relation.
The power consumed by a resistive device is given by:
Rearranging to solve for : Step 2: Substitute the given values.

Step 1: Convert Power from Watts to Kilowatts
Power is usually given in watts (W), but for calculating energy consumption in kilowatt-hours (kWh), it needs to be converted to kilowatts (kW).
100 watts = 100 ÷ 1000 = 0.1 kW

Step 2: Calculate Total Time of Usage
Suppose the electrical device is used for 5 hours per day over a period of 30 days:
Total usage time = 5 hours/day × 30 days = 150 hours

Step 3: Calculate Energy Consumed
Energy consumed (E) is calculated using the formula:
Energy (kWh) = Power (kW) × Time (hours)
Substituting the values:
E = 0.1 kW × 150 hours = 15 kWh

Final Answer:
15 kilowatt-hours (kWh)