For obtaining wattless current,……. is connected with AC supply.}
Step 1: Understanding Wattless Current
Wattless current refers to the condition when the power consumed in an AC circuit is zero. The power in an AC circuit is given by: \[ P = VI \cos \phi \] where:
- \( P \) is the power,
- \( V \) is the voltage,
- \( I \) is the current,
- \( \phi \) is the phase difference between voltage and current.
Step 2: Condition for Wattless Current
- Power consumption in a circuit depends on the power factor \( \cos \phi \).
- If \( \phi = 90^\circ \), then: \[ \cos 90^\circ = 0 \] which means: \[ P = 0 \] - This happens when the circuit contains a pure inductor (L) or pure capacitor (C), as they store and release energy without dissipating power.
Step 3: Conclusion
- A pure inductor (L) or pure capacitor (C) does not consume power but still allows alternating current to flow.
- Since the given question specifically asks for wattless current, the correct answer is only \( L \) (Inductor).
A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force \( F = 20 \, \text{N} \) acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take \( g = 10 \, \text{m/s}^2 \)):
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]