The potential difference between the terminals of an electrical heating device is 40 V, when it draws a current of 2 A from the source. Which one of the following is the correct value of current drawn by the heating device if the potential is increased to 140 V?
- (a)7 A
- (b)5 A
- (c)4 A
- (d)2 A
Correct — A, 7 A. The device obeys Ohm's law, so its resistance is fixed and can be found from the first pair of readings: R = V/I = 40 V divided by 2 A, which is 20 ohms. At the new potential difference the same resistance gives I = V/R = 140 V divided by 20 ohms, which is 7 A. The shortcut is that current is directly proportional to potential difference when resistance is constant, and 140 volts is 3.5 times 40 volts, so the current must also be 3.5 times 2 A — again 7 A.
- (b)5 A — Does not follow from any consistent reading of the data. A current of 5 A at 140 V would mean a resistance of 28 ohms, but the first pair of readings fixes the resistance at 20 ohms.
- (c)4 A — Looks like the result of doubling the current because the voltage has roughly tripled and then rounding, or of dividing 140 by 35. Neither operation is Ohm's law, and 4 A at 140 V would imply a resistance of 35 ohms.
- (d)2 A — Assumes the current is unchanged when the potential difference is raised. That would require the resistance to rise with voltage in exact proportion, which is what an ohmic device does not do.
Ohm's law states that for a conductor at constant temperature, the current through it is directly proportional to the potential difference across it, so V = IR with R constant. That constant is the resistance and it depends on the material, length, cross-section and temperature of the conductor, not on the applied voltage. Any question that gives one voltage-current pair and asks for a second is really asking you to extract R once and reuse it, or equivalently to scale the current by the same factor as the voltage.
The whole item is one division and one multiplication, so the risk is arithmetic rather than physics. Check the ratio: 140 divided by 40 is 3.5, and 3.5 multiplied by 2 is 7, which agrees with the direct calculation. It is worth noting the physical caveat that examiners occasionally exploit — a heating device run at 3.5 times its rated voltage would get much hotter, and in a real filament resistance rises with temperature, so a laboratory measurement would fall short of 7 A. The question, however, treats the device as ohmic, and that is the intended reading. This card marks a different letter from the answer we hold on file.
- Ohm's law: V = IR, with R constant for a given conductor at a given temperature.
- Resistance from the first reading is 40 V divided by 2 A, that is 20 ohms.
- At 140 V the same 20 ohms carries 140 divided by 20, that is 7 A.
- Current is directly proportional to voltage when resistance is constant, so a 3.5-fold rise in voltage gives a 3.5-fold rise in current.
- Resistance depends on material, length, area of cross-section and temperature, not on the applied potential difference.
Both routes give the same figure, which is the quickest way to be sure the arithmetic has not slipped.
- Assuming the current stays the same when the voltage changes.
- Adding the voltage difference to the current instead of scaling by the ratio.
- Forgetting to check the answer by proportion, which catches almost every arithmetic slip in this kind of item.
A two-step numerical that tests only whether Ohm's law is applied with a constant resistance; the numbers are chosen to divide exactly.
Which one of the following statements regarding Ohm's law is not correct?
- (a) Ohm's law is an assumption that current through a conductor is always directly proportional to the potential difference applied to it.
- (b) A conducting device obeys Ohm's law when the resistance of a device is independent of magnitude and polarity of applied potential difference.
- (c) A conducting material obeys Ohm's law when the resistance of material is independent of the magnitude and direction of applied electric field.
- (d) All homogeneous materials obey Ohm's law irrespective of whether the field is within range or strong.
Answer(d) All homogeneous materials obey Ohm's law irrespective of whether the field is within range or strong.
Sets the limits of the rule this calculation uses. Ohm's law is an empirical relation that holds for certain materials under certain conditions, which is why the constant-resistance assumption here has to be stated rather than assumed universally.
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
The same law used the other way round, on resistance rather than current. Both items reward extracting the constant first and only then substituting.
- practice — not a real PYQ
A resistor carries 0.5 A when 10 V is applied across it. What current will flow if the potential difference is raised to 25 V?
- (a)1.0 A
- (b)1.25 A
- (c)1.5 A
- (d)2.5 A
Answer(b) 1.25 A — the resistance is 10/0.5 = 20 ohms, so at 25 V the current is 25/20 = 1.25 A.
- practice — not a real PYQ
The resistance of a metallic conductor does not depend on
- (a)its length
- (b)its area of cross-section
- (c)the potential difference applied across it
- (d)its temperature
Answer(c) the potential difference applied across it — for an ohmic conductor the resistance is a property of the conductor, not of the applied voltage.