The graphs between current (I) and voltage (V) for three linear resistors 1, 2 and 3 are given below : If R₁, R₂ and R₃ are the resistances of these resistors, then which one of the following is correct?
- (a)R₁ > R₂ > R₃
- (b)R₁ < R₃ < R₂
- (c)R₃ < R₁ < R₂
- (d)R₃ > R₂ > R₁
Answer
Why
Correct — B, R₁ < R₃ < R₂. The printed graph has current I up the vertical axis and voltage V along the horizontal, with three straight lines all starting at the origin. Line 1 is the steepest, line 3 lies in the middle, and line 2 is the shallowest — that ordering is what the whole item turns on.
For a linear (ohmic) resistor, V = IR, so I = V/R. Plotted as I against V that is a straight line through the origin whose slope is 1/R, not R. Resistance is therefore the reciprocal of the slope: the steeper the line, the smaller the resistance.
Steepest line 1 gives the smallest resistance, middle line 3 the middle value, and shallowest line 2 the largest. So R₁ < R₃ < R₂.
Why the others are wrong
- (a)R₁ > R₂ > R₃ — This reads the slope as the resistance itself, so the steepest line is called the largest resistance. On an I–V plot the slope is 1/R, so the order is exactly reversed.
- (c)R₃ < R₁ < R₂ — This puts line 3 below line 1. Line 1 is the steeper of the two, so it has the larger 1/R and therefore the smaller resistance — R₁ is the smallest, not R₃.
- (d)R₃ > R₂ > R₁ — It gets R₁ smallest, which is right, but then places R₃ above R₂. Line 2 is shallower than line 3, so R₂ is the largest of the three.
Concept
Ohm's law, V = IR, makes a linear resistor's current-voltage graph a straight line through the origin. Which quantity the slope represents depends on which variable is on which axis. With I on the vertical axis and V on the horizontal, the slope is I/V = 1/R, the conductance. With the axes swapped — V vertical, I horizontal — the slope is the resistance R itself.
The trap is answering from the picture without checking the axes. 'Steeper means bigger' is a safe instinct for most graphs and it is wrong here, because the plotted slope is the reciprocal of the quantity being ranked. Read the axis labels first, decide whether the slope is R or 1/R, and only then rank the lines. A reliable habit is to pick one voltage, read off the three currents, and use R = V/I directly — the line giving the largest current at that voltage must have the smallest resistance.
Key facts
- For an ohmic resistor, V = IR gives a straight line through the origin.
- On an I-versus-V plot the slope equals 1/R, so R = 1/slope.
- On a V-versus-I plot the slope equals R.
- Steeper line on an I–V graph means smaller resistance.
- Here line 1 is steepest and line 2 shallowest, so R₁ < R₃ < R₂.
Slope on an I–V plot is 1/R, so the ranking of resistances reverses the ranking of steepness — R₁ < R₃ < R₂, option (b).
Study next
Common traps
- Assuming the steeper line always means the larger quantity.
- Not checking which variable is on which axis before using the slope.
- Confusing conductance (1/R) with resistance.
NDA prints two or three straight I–V lines and asks you to rank the resistances — identify from the axes whether the slope is R or 1/R, then rank accordingly.
Related PYQs
An electric wire of resistance 50 ohm is cut into five equal wires. These wires are then connected in parallel. What is the equivalent resistance of this combination?
- (a) 2 ohm
- (b) 10 ohm
- (c) 0·5 ohm
- (d) 5 ohm
Answer(a) 2 ohm
Ohm's law applied to a wire cut and re-paralleled — the same V = IR relation, used numerically rather than graphically.
Practice
- practice — not a real PYQ
On a graph of voltage (V) against current (I) for an ohmic conductor, the slope of the straight line represents
- (a)the conductance
- (b)the resistance
- (c)the power dissipated
- (d)the current density
Answer(b) the resistance — with V on the vertical axis and I on the horizontal, slope = V/I = R. - practice — not a real PYQ
Two ohmic resistors are plotted on the same I–V graph. Line P is steeper than line Q. Which statement is correct?
- (a)P has the greater resistance
- (b)Q has the greater resistance
- (c)Both have equal resistance
- (d)Resistance cannot be compared from the graph
Answer(b) Q has the greater resistance — slope on an I–V plot is 1/R, so the shallower line Q has the larger R.