V-I graph for a platinum wire at temperatures \( T_1 \) and \( T_2 \) is shown in the given figure. The temperature difference \( (T_2 - T_1) \) is proportional to:
\( \cot 2\theta \)
The slope of the V-I graph is related to the resistance \( R \), which in turn depends on temperature. The temperature difference \( (T_2 - T_1) \) is proportional to \( \cot 2\theta \), as resistance increases with temperature following the relation:
\[ R = R_0 (1 + \alpha (T - T_0)) \]
where \( \alpha \) is the temperature coefficient of resistance. This leads to the dependence on \( \cot 2\theta \), making option 4 correct.
Important Questions from Current Electricity
The current through a 4/3 Ω external resistance connected to a parallel combination of two cells of 2 V and 1 V emf and internal resistances of 1 Ω and 2 Ω respectively is:
A metallic wire of uniform area of cross-section has a resistance R, resistivity ρ, and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity, and power rating at V volts are now denoted by R', ρ', and P' respectively. The corresponding values are correctly related as:
A cell of emf 1.1 V and internal resistance 0.5 Ω is connected to a wire of resistance 0.5 Ω. Another cell of the same emf is now connected in series with the intention of increasing the current, but the current in the wire remains the same. The internal resistance of the second cell is:
P, Q, R, and S are four wires of resistances 3 Ω, 3 Ω, 3 Ω, and 4 Ω, respectively. They are connected to form the four arms of a Wheatstone bridge circuit. The resistance with which S must be shunted in order that the bridge may be balanced is:
The magnetic moment of a thin bar magnet is 'M'. If it is bent into a semicircular form, its new magnetic moment will be:
