Consider 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.
1. Both the statements are correct
2. Both the statements are incorrect
3. Only statement A is correct
4. Only statement B is correct
View Answer
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.
A 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
1. \(10^5\text{ A/m}^2\)
2. \(10^6\text{ A/m}^2\)
3. \(2 \times 10^5\text{ A/m}^2\)
4. \(2 \times 10^6\text{ A/m}^2\)
View Answer
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 \(J = \sigma E = 10^5 \times 10 = 10^6\text{ A/m}^2\).
Consider 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.
1. Only statement (A) is correct
2. Only statement (B) is correct
3. Both statements are correct
4. Both statements are incorrect
View Answer
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.
Estimate 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 \(8.5 \times 10^{28}\text{ m}^{-3}\).
1. \(2.2\text{ mm s}^{-1}\)
2. \(1.1\text{ mm s}^{-1}\)
3. \(3.3\text{ mm s}^{-1}\)
4. \(0.1\text{ mm s}^{-1}\)
View Answer
Using the formula for drift velocity \(v_d = \frac{I}{n e A}\), we substitute the given values: \(v_d = \frac{1.5}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 10^{-7}} \approx 1.1 \times 10^{-3}\text{ m/s} = 1.1\text{ mm s}^{-1}\).
A maximum current can be drawn from a cell when
1. Cell is open
2. Cell is connected with a finite external resistance
3. External resistance is equal to internal resistance
4. Cell is short circuited
View Answer
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.
A 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
1. \(9988\ \Omega\) in parallel
2. \(9988\ \Omega\) in series
3. \(10000\ \Omega\) in parallel
4. \(10000\ \Omega\) in series
View Answer
To convert a galvanometer into a voltmeter, a high resistance \(R\) is connected in series: \(V = I_g(G + R) \implies 10 = 10^{-3}(12 + R) \implies R = 9988\ \Omega\).