Question 141:
easyConsider the following statements and choose the correct option.
Statement A: Energy is dissipated inside a battery due its internal resistance.
Statement B: In a resistor, current flows from higher potential to lower potential.
Statement A is correct because the internal resistance of a cell causes Joule heating inside it. Statement B is correct because in passive elements like resistors, conventional current flows down potential gradients.
Question 142:
easyA copper wire of length \(1\text{ m}\) and radius \(\left(\frac{10^{-3}}{\sqrt{\pi}}\right)\text{ m}\) has electrical resistance of \(10\ \Omega\). The current density in the wire for an electric field strength of \(10\text{ V/m}\) is
Area \(A = \pi r^2 = 10^{-6}\text{ m}^2\). Resistivity \(\rho = RA/l = 10 \times 10^{-6} / 1 = 10^{-5}\ \Omega\cdot\text{m}\). Conductivity \(\sigma = 1/\rho = 10^5\text{ S/m}\). Current density is \(J = \sigma E = 10^5 \times 10 = 10^6\text{ A/m}^2\).
Question 143:
easyConsider the following statements and choose the correct option.
Statement (A): Kirchhoff’s junction law follows the conservation of charge.
Statement (B): Kirchhoff’s loop law follows the conservation of energy.
Kirchhoff's first law (junction rule) is based on the law of conservation of charge, while the second law (loop rule) is based on the law of conservation of energy. Both statements are correct.
Question 144:
moderateEstimate the average drift speed of conduction electrons in a conductor of cross-sectional area \(10^{-7}\text{ m}^2\) carrying current of \(1.5\text{ A}\). The number density of conduction electrons is \(8.5 \times 10^{28}\text{ m}^{-3}\).
Using the formula for drift velocity \(v_d = \frac{I}{n e A}\), we substitute the given values: \(v_d = \frac{1.5}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 10^{-7}} \approx 1.1 \times 10^{-3}\text{ m/s} = 1.1\text{ mm s}^{-1}\).
Question 145:
easyA maximum current can be drawn from a cell when
The current in a circuit is \(I = \frac{E}{R + r}\). Current is maximized when the external resistance \(R = 0\), which corresponds to a short-circuited cell.
Question 146:
moderateA galvanometer coil has a resistance of \(12\ \Omega\) and the meter show full scale deflection for a current of \(1\text{ mA}\). The resistance required to be added to convert the galvanometer into a voltmeter of range \(0\) to \(10\text{ V}\) will be
To convert a galvanometer into a voltmeter, a high resistance \(R\) is connected in series: \(V = I_g(G + R) \implies 10 = 10^{-3}(12 + R) \implies R = 9988\ \Omega\).
Question 147:
easyCopper and silicon is cooled from $300 \text{ K}$ to $60 \text{ K}$, the specific resistance:
(2001)
Copper is a metal, and its specific resistance decreases with a decrease in temperature. Silicon is a semiconductor, and its specific resistance increases as temperature decreases.
Question 148:
easyThree copper wires of lengths and cross-sectional areas are $(l, A)$, $(2l, A/2)$ and $(l/2, 2A)$. Resistance is minimum in
(1997)
Resistance $R = \rho \frac{l}{A}$. For the three wires: $R_{1} = \rho \frac{l}{A}$, $R_{2} = \rho \frac{2l}{A/2} = 4\rho \frac{l}{A}$, and $R_{3} = \rho \frac{l/2}{2A} = \frac{1}{4}\rho \frac{l}{A}$. The minimum resistance is for the wire with area $2A$.
Question 149:
easy2. A flow of $10^{7}$ electrons per second in a conducting wire constitutes a current of (1994)
Current $I = \frac{q}{t} = \frac{ne}{t}$. Given $\frac{n}{t} = 10^{7} \text{ s}^{-1}$. Thus, $I = 10^{7} \times 1.6 \times 10^{-19} = 1.6 \times 10^{-12} \text{ A}$.
Question 150:
easy3. The velocity of charge carriers of current (about $1 \text{ ampere}$) in a metal under normal conditions is of the order of (1991)
The drift velocity of electrons in a typical metallic conductor under normal conditions is extremely small, typically on the order of $10^{-4} \text{ m/s}$ or a fraction of a $\text{mm/sec}$.