On which factors and how do the following depend?
(i) Internal resistance of cell
(ii) Resistance of conductor
i. Internal resistance of cell Step 1: The internal resistance of a cell depends on several factors: \[ r \propto \frac{\text{distance between electrodes}}{\text{area of electrodes}} \] - It increases if the distance between electrodes increases.
- It decreases if the cross-sectional area of electrodes increases.
- It depends on the electrolyte's concentration and nature. \[ \text{Thus, the internal resistance can be minimized by using a highly conductive electrolyte and optimizing electrode placement.} \] \[ \boxed{\text{Factors: Distance, area, electrolyte nature, and temperature}} \]
ii. Resistance of conductor
Step 1: The resistance of a conductor is given by: \[ R = \rho \frac{L}{A} \] where: - \( R \) is resistance,
- \( \rho \) is resistivity,
- \( L \) is length,
- \( A \) is cross-sectional area.
Step 2: Factors affecting resistance: - It increases with an increase in length (\( L \)).
- It decreases with an increase in cross-sectional area (\( A \)).
- Different materials have different resistivities.
- Resistance increases with temperature due to an increase in resistivity. \[ \text{Therefore, resistance can be controlled by choosing appropriate materials and dimensions.} \] \[ \boxed{\text{Factors: Length, cross-sectional area, material, and temperature}} \]
The switch (S) closes at \( t = 0 \) sec. The time, in sec, the capacitor takes to charge to 50 V is _________ (round off to one decimal place).
The op-amps in the following circuit are ideal. The voltage gain of the circuit is __________(round off to the nearest integer).
In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at \( F \) very close to circuit breaker 1. The circuit breakers open to isolate the line. The fault self-clears. The circuit breakers reclose and restore the line. Which one of the following diagrams best indicates the rotor accelerating and decelerating areas?
The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is “abc”. The primary to secondary turns ratio is 2:1. If \( I_a + I_b + I_c = 0 \), then the relationship between \( I_A \) and \( I_{ad} \) will be:
In the circuit shown below, if the values of \( R \) and \( C \) are very large, the form of the output voltage for a very high frequency square wave input is best represented by:
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $