A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.
Question: 1
If resistor X were made of manganin and readings for V and I are taken without switching off the circuit, the graph between V and I will be as :
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Alloys like manganin and constantan are specifically utilized to manufacture standard resistance coils because their resistance values are highly immune to temperature variations. Consequently, their $I$-$V$ characteristics always yield a perfect linear relationship (straight line passing through the origin), adhering strictly to Ohm's law.
Error in the value of X obtained from different sets of voltmeter and ammeter readings, is :
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Whenever a calculated quantity involves a multiplication or division of variables (such as $R = V/I$ or $\rho = R A / L$), always add the relative or percentage errors of each component together to determine the total maximum error. Errors are never subtracted or divided.
equal to the sum of error in voltmeter reading and error in ammeter reading.
equal to error in voltmeter reading divided by the error in ammeter reading.
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The Correct Option isC
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Question: 3
If the movable end of rheostat is moved towards P, then :
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Reducing resistance in a single-loop series circuit always increases the global loop current. For any fixed resistor in that loop, a higher loop current translates directly to a larger individual potential drop ($V = IR$). Hence, both the ammeter and voltmeter readings go up.
reading in ammeter decreases and reading in voltmeter increases.
readings in both voltmeter and ammeter increase.
reading in ammeter increases and reading in voltmeter decreases.
readings in both voltmeter and ammeter decrease.
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The Correct Option isB
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Question: 4
Suppose the unknown resistance X is replaced by a wire made of the same metal. This wire consists of three parts, of the same length L but has radii r, r/3 and r/2 as shown in the figure. For a particular setting of the rheostat, let \(v_1\), \(v_2\) and \(v_3\) be the value of drift velocities in parts AC, CD and DB. Then :
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For conductors connected in series carrying a steady current, the drift velocity of charge carriers is inversely proportional to the cross-sectional area (\(v_d \propto 1/A \propto 1/r^2\)). Therefore, narrower sections always exhibit faster drift velocities to maintain a constant current flow.
Consider the same wire, as shown in figure in question (iv) (a) connected in place of X. For a particular setting of rheostat, let \(E_1\), \(E_2\) and \(E_3\) be the value of electric fields in part AC, CD and DB. Then :
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For a continuous series conductor of a given material, both the electron drift velocity and the internal electric field follow the exact same structural dependence: they are inversely proportional to the cross-sectional area (\(E \propto 1/A\) and \(v_d \propto 1/A\)). Consequently, their mathematical order profiles are identical.
