Electrical Instruments

Step 1: To find the point where the electric field is zero, we must equate the electric fields due to both charges. The electric field due to a point charge is given by: where is Coulomb's constant, is the charge, and is the distance from the charge. The point where the electric field becomes zero is where the magnitudes of the fields from both charges are equal, so: After solving the equation, we get the value .

Step 1: Using the Temperature Dependence Formula
The resistance of a wire at a given temperature is given by: where: - = Resistance at temperature , - (Resistance at reference temperature ), - (Temperature coefficient of resistance), - (New temperature).

Step 2: Substituting the Values

Step 3: Conclusion
Thus, the resistance of the wire at is:

Step 1: Understanding Closest Distance of Approach The closest distance of approach of an particle in Rutherford scattering is given by: where:
- is the atomic number of the nucleus,
- is the charge of the electron,
- is the initial kinetic energy of the particle.

Step 2: Effect of Doubling Speed Kinetic energy is related to speed as: If the initial speed of the particle is doubled: Since is inversely proportional to : Thus, the closest distance of approach becomes one-fourth of its original value. Thus, the correct answer is becomes one-fourth.

Step 1: In a meter bridge, the balance length is given by the formula: where and are the resistances in the two gaps.

Step 2: If the resistance in the right gap is doubled, the new balance length is adjusted.

Step 3: The change in the balancing length is found to be .

Step 1: Using the Formula for Magnetic Moment of a Coil The magnetic moment of a current-carrying coil is given by: where:
- (number of turns),
- A (current in the coil),
- (area of cross-section).

Step 2: Substituting Values Thus, the correct answer is .

In a rectifier circuit, the capacitor is used to smooth out the variations in the rectified current, making the output steady. This helps in converting the pulsating DC into a smooth, steady DC.

Step 1: The capacitor connected across the rectifier output helps in filtering the ripple and gives a steady DC output. This is essential for powering devices that require constant DC voltage. Thus, the correct answer is to get a steady DC output.

The loss of strength of a signal during propagation is referred to as attenuation. This happens due to energy loss, resistance in the medium, and other factors that weaken the signal as it travels.

Step 1: Attenuation refers to the reduction in the amplitude and strength of the signal as it travels through the medium, whether in wires or free space. This is a common phenomenon in communication systems. Thus, the correct answer is attenuation. \bigskip

Step 1: Understanding AC Circuit Voltage Relations For an AC circuit consisting of a resistor (R) and inductor (L) in series, the total voltage ( ) is given by the phasor sum of the voltage across the resistor ( ) and the inductor ( ): where: - = total voltage supplied by the AC source = V - = voltage across the inductor = V - = voltage across the resistor (to be determined)

Step 2: Applying the Phasor Equation Thus, the potential difference across the resistor is: