विद्युतचुंबकत्व

Analysis of the circuit with the voltmeter connected:

• Two resistors of $100\,\Omega$ each are in series across a $40\,\text{V}$ DC supply.
• The voltmeter of resistance $R_V = 150\,\Omega$ is connected in parallel with the first $100\,\Omega$ resistor (across points A and B).

• Step 1: Calculate the equivalent resistance between A and B ($R_{AB}$):
  $$R_{AB} = \frac{100 \times 150}{100 + 150} = \frac{15000}{250} = 60\,\Omega$$
• Step 2: Total resistance of the circuit:
  $$R_{\text{total}} = R_{AB} + R_{BC} = 60\,\Omega + 100\,\Omega = 160\,\Omega$$
• Step 3: Total current in the circuit:
  $$I = \frac{V_{\text{total}}}{R_{\text{total}}} = \frac{40\,\text{V}}{160\,\Omega} = 0.25\,\text{A}$$
• Step 4: Reading of the voltmeter (potential difference across AB):
  $$V_{AB} = I \times R_{AB} = 0.25\,\text{A} \times 60\,\Omega = 15\,\text{V}$$

The drift velocity of conduction electrons in a conductor of length $l$ under an applied potential difference $V$ is given by:

where:

• $e$ is electron charge
• $m$ is electron mass
• $\tau$ is relaxation time
• $V$ is applied voltage
• $l$ is conductor length

For a given conductor at constant temperature, $v_d \propto V$. Hence, option 2 is the correct answer.

In semiconductors, the charge carrier density $n$ increases exponentially with temperature:

Since resistivity is inversely proportional to carrier density:

As temperature $T$ increases, resistivity $\rho$ decreases rapidly (exponential decay).

Graph 3 correctly represents this non-linear exponential decrease of resistivity with temperature.