An electric motor is connected to an electric source of emf 'E' having internal resistance r Ω. The power consumed by the motor, if the current drawn is E/2r, will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → E2/4r
Note: The given answer is as per the official NTA Answer Key. However, the question can have more than one correct answer, i.e. both Option (2) and Option (3), as explained below.
The source supplies power EI; part of it, \( I^{2}r \), is lost in the internal resistance and the rest is consumed by the motor.
\( \displaystyle I = \frac{E}{2r} \)
\( \displaystyle P_{\mathrm{source}} = EI = \frac{E^{2}}{2r} \)
\( \displaystyle P_{\mathrm{loss}} = I^{2}r = \frac{E^{2}}{4r^{2}} \times r = \frac{E^{2}}{4r} \)
\( \displaystyle P_{\mathrm{motor}} = \frac{E^{2}}{2r} - \frac{E^{2}}{4r} = \frac{E^{2}}{4r} \)
Option (2) I2r — Correct. With \( I = E/2r \), \( I^{2}r = E^{2}/4r \), the same value as the motor’s power, although strictly \( I^{2}r \) is the heat produced in the internal resistance.
Option (3) E2/4r — Correct. This is the power consumed by the motor, worked out above.