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Which of the following is a disadvantage of using the phasor diagram method for analyzing AC circuits?
The NCERT text states, 'This method of analysing ac circuits suffers from certain disadvantages. First, the phasor diagram say nothing about the initial condition.'
The phase angle $\phi$ for a series RLC circuit, which determines the phase difference between the source voltage and the current, can be determined using the formula:
The NCERT text (Eq. 7.27) states, '$\tan\phi = \frac{X_C - X_L}{R}$'.
A phasor is defined as a vector that rotates about the origin. What does its angular speed represent?
The NCERT text defines a phasor as 'a vector which rotates about the origin with angular speed $\omega$'.
In a series RLC circuit, the current phasor I is commonly drawn horizontally as a reference. In this representation, where would the voltage phasor across the resistor (VR) be located?
The NCERT notes that in an RLC circuit, 'VR is parallel to I'. This means they are in phase and drawn in the same direction on a phasor diagram.
If the voltage across an AC source is given by $v = v_m \sin(\omega t)$ and the current in a particular circuit element is $i = i_m \sin(\omega t + \pi/2)$, which type of element is predominant in determining the phase relationship?
The current waveform $i = i_m \sin(\omega t + \pi/2)$ indicates that the current leads the voltage by $\pi/2$. This phase relationship is characteristic of a purely capacitive circuit, where the current through the capacitor is $\pi/2$ ahead of the applied voltage.
In a series RLC circuit, the individual voltage phasors V_L, V_R, and V_C combine to form the total voltage phasor V. If V_C and V_L are always along the same line and in opposite directions, what is the magnitude of their combined phasor $(V_C + V_L)$?
The NCERT text states, 'Since VC and VL are always along the same line and in opposite directions, they can be combined into a single phasor (VC + VL) which has a magnitude $|v_{Cm} – v_{Lm}|$.' This corresponds to $|V_C - V_L|$ for the RMS or peak voltage magnitudes.
The analysis of an AC circuit is simplified by using phasor diagrams because:
The NCERT text highlights this benefit: 'The analysis of an ac circuit is facilitated by the use of a phasor diagram.' And further explains, 'The rotating vectors that represent harmonically varying scalar quantities are introduced only to provide us with a simple way of adding these quantities using a rule that we already know as the law of vector addition.'
Which of the following values correctly represents the universal gravitational constant (G) as mentioned in the provided text?
The provided text in problem 7.17 and 7.19 explicitly states 'G = $6.67 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}$'. The other options represent acceleration due to gravity, mass of Earth, and radius of Earth respectively.
The value of the universal gravitational constant, G, is used in determining the mass of the Earth. This determination is attributed to whose experiment, as per the text?
The text on page 133, under section 7.5, states: 'The measurement of G by Cavendish’s experiment (or otherwise), combined with knowledge of g and R_E enables one to estimate M_E from Eq. (7.12). This is the reason why there is a popular statement regarding Cavendish : “Cavendish weighed the earthâ€.'
According to the provided text, if the zero of potential energy is at infinity ($r \rightarrow \infty$), what is the nature of the gravitational potential energy of an object at a finite distance?
Points to Ponder, point 6, and page 135 state: 'Relative to infinity (i.e. if we presume that the potential energy of the object at infinity is zero), the gravitational potential energy of an object is negative.' and 'V = - $G m_1 m_2 / r$ (if we choose V = 0 as $r \rightarrow \infty$ )'. Since G, $m_1$, $m_2$, and r are positive, the expression - $G m_1 m_2 / r$ will always be negative.
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.