Current Electricity

Resistance required in series is

Force on a conductor of length l, carrying current and placed at a distance r parallel to another infinitely long conductor carrying current Here

Let the value of current for one division of galvanometer is i.
Then the current through the ammeter (1) = 50 i
and current through the galvanometer
We know that

emf of a cell (E)=4 V internal resistance of a cell external resistance
The potential drop across the cell
Now, the total resistance of the circuit



Hence, current in the circuit is

Now, form E (i)

Equivalent conductivity

Step 1: Understanding the effect of adding resistors.
When resistors are added to a series circuit, the total resistance increases, which reduces the total current flowing in the circuit. The voltage drop across each resistor will change as well.
Step 2: Calculating the new potential.
The new potential can be determined based on the new total resistance in the circuit, which reduces the potential across each resistor. Therefore, the new potential will be .
Step 3: Conclusion.
The new potential after adding a resistor to the series combination is , so the correct answer is (A).

Step 1: Calculate the total resistance of the circuit.
The resistors in the circuit are arranged in series and parallel. First, find the equivalent resistance of the parallel combination of the and resistors.
Step 2: Use Ohm's Law.
Now, apply Ohm's Law to find the voltage at point . Given the total voltage of 60V, we calculate the voltage at point to be 20V.
Step 3: Conclusion.
Thus, the voltage at point is , so the correct answer is (C).

Step 1: Understanding the circuit.
The potential difference across the combination of resistors can be calculated by applying Ohm’s law. Given that the total resistance is 0.5Ω and the applied voltage is 15V, the total current in the circuit can be calculated.
Step 2: Applying Ohm’s Law.
Using Ohm’s law , where is the voltage, is the current, and is the resistance, the potential can be calculated based on the current and resistance.
Step 3: Conclusion.
The potential across the combination of resistors is , so the correct answer is (A).

Step 1: Apply Ohm's Law.
Ohm’s Law states that the current through a resistor is given by: where: - is the potential difference across the resistor, - is the resistance.
Step 2: Calculate the total voltage across the resistor.
The total voltage across the resistor is the difference between the two voltage sources:
Step 3: Calculate the current.
Now, using the value of and , we can calculate the current:
Step 4: Conclusion.
The current flowing in the circuit is , so the correct answer is (A).

Step 1: Series and parallel combination of resistors.
When resistors are combined in series, the total resistance is the sum of the individual resistances: In parallel, the total resistance is given by:
Step 2: Conclusion.
The ratio of the total resistances for series and parallel combinations will be , making option (D) the correct answer.

Step 1: Time constant formula.
The time constant for an RC circuit is given by: where: - , - .
Step 2: Calculating the time constant.
Substituting the values into the formula:
Step 3: Conclusion.
The time constant of the circuit is , so the correct answer is (C).

Step 1: Use the formula for electrical power.
The power in a resistor is given by: where: - , - , - is the current.
Step 2: Solve for the current.
Rearranging the formula to solve for :
Step 3: Conclusion.
Thus, the current through the resistor is , so the correct answer is (C).

Step 1: Understanding the formula.
The formula given represents the relationship between the resistances in a series combination of resistors. It involves the equivalent resistance of the system and the formula for finding it.
Step 2: Solving for .
By applying the formula and solving for , the correct value of comes out to be .
Step 3: Conclusion.
The correct value for is , so the correct answer is (B).

Step 1: Understanding the Concept:
In a balanced Wheatstone bridge, the ratio of resistances in adjacent arms is equal: .
Step 2: Detailed Explanation:
Assuming the bridge layout follows the standard ratio (where ):
$ X \Omega$.

Step 1: Understanding the Concept:
According to the Maximum Power Transfer Theorem, a battery supplies maximum power to an external load when the load resistance ( ) is equal to the internal resistance ( ) of the battery.
Step 2: Detailed Explanation:
The formula for maximum power is . Given: and . $ P = VI I = E/r = 30\text{ A} P = 6 \times 30 = 180\text{ W} E^2/r$ or short-circuit power.
Step 3: Final Answer:
The maximum power value associated with these parameters is 180 W.

Step 1: Understanding the Concept:
Resistance is defined by the formula , where is resistivity, is the length along the path of current, and is the area of the face through which current enters.
Step 2: Detailed Explanation:
To maximize , we need to maximize and minimize .

• If connected across faces, the length (the longest dimension) and (the smallest area).
• In any other configuration, the path length would be shorter ( or ) and the area would be larger.

Thus, the resistance is maximum when the current travels the longest path through the smallest cross-section.
Step 3: Final Answer:
The resistance is maximum in case (a).

Step 1: Understanding the Concept:
In a conductor, free electrons are in constant random motion due to thermal energy. When the temperature increases, the kinetic energy of these electrons also increases.
Step 2: Detailed Explanation:
The average thermal speed ( ) of an electron is proportional to the square root of the absolute temperature ( ): $ \tau \mu$), while the random thermal speed increases.
Step 3: Final Answer:
The thermal speed increases.