If the current through an electrical machine running on direct current is 15 A and the machine runs for 10 minutes, the charge that passes through the machine during this time is:
- (a)1·50 C
- (b)150 C
- (c)900 C
- (d)9000 C
Correct — D, 9000 C. Electric current is the rate at which charge flows, I = Q/t, so the charge is Q = I x t. The current is steady at 15 A and the time must be in seconds, so 10 minutes = 10 x 60 = 600 s. Therefore Q = 15 A x 600 s = 9000 coulombs.
- (a)1·50 C — 1.50 C comes from dividing instead of multiplying (15 ÷ 10) or otherwise mishandling the numbers. Charge is current MULTIPLIED by time, and with a 15 A current for several minutes the charge must be far larger than one coulomb.
- (b)150 C — 150 C = 15 x 10 uses the time as 10 (minutes) without converting to seconds. Current is defined per second, so the 10 minutes must first become 600 s; skipping this undercounts by a factor of 60.
- (c)900 C — 900 C = 15 x 60 uses only 60 s (one minute) instead of the full 10 minutes. The machine runs for 10 minutes = 600 s, so the correct product is 15 x 600 = 9000 C.
Electric current is the rate of flow of electric charge past a point, I = Q/t. Rearranged, the charge transported by a steady current is Q = I x t. This is the operational definition behind the ampere, and it applies to any device carrying a constant direct current.
The only trap here is units: the time given in minutes must be converted to seconds before multiplying, because one ampere is one coulomb per second. Convert first (10 min = 600 s), then multiply by the steady 15 A. A quick sanity check is that a large current over several minutes must transfer thousands of coulombs, ruling out the small options.
- Current is the rate of flow of charge, I = Q/t, so charge Q = I x t.
- In SI units one ampere equals one coulomb per second, so 1 C = 1 A x 1 s.
- Time must be in seconds before multiplying: 10 minutes = 600 s.
- Q = 15 A x 600 s = 9000 C.
- One coulomb is the charge of about 6.24 x 10^18 electrons, since the elementary charge e ≈ 1.6 x 10^-19 C.
- Leaving the time in minutes instead of converting to seconds.
- Dividing current by time instead of multiplying.
- Converting only part of the time (using one minute instead of ten).
NDA/UPSC give a steady current and a running time (often in minutes) and ask for the charge — always convert time to seconds and use Q = I x t.
No directly related past PYQ was found.
- practice — not a real PYQ
A steady current of 2 A flows through a wire for 5 minutes. The charge that passes through it is
- (a)10 C
- (b)600 C
- (c)1000 C
- (d)6000 C
Answer(b) 600 C — Q = I x t = 2 A x (5 x 60) s = 2 x 300 = 600 C.
- practice — not a real PYQ
How much charge flows through a device when a current of 0.5 A passes for 1 hour?
- (a)30 C
- (b)180 C
- (c)1800 C
- (d)3600 C
Answer(c) 1800 C — Q = I x t = 0.5 A x 3600 s = 1800 C.