Question

A battery of 10 volt carries 20,000 C of charge through a resistance of \(20\ \Omega\). The work done in 10 seconds is

• A. \(2 \times 10^5\text{ joule}\)
• B. \(2 \times 10^3\text{ joule}\)
• C. \(2 \times 10^6\text{ joule}\)
• D. \(2 \times 10^4\text{ joule}\)

Hint:

Be careful of distractor variables!
The resistance (\(20\ \Omega\)) and time (\(10\text{ s}\)) are given to distract you.
The fundamental definition of potential difference is \(V = W/Q\), which does not depend on time or resistance.

Answer 1

The Correct Option is A

Step 1: Work out the average current first.
A charge of $Q = 20{,}000\text{ C}$ passes through the circuit in $t = 10\text{ s}$, so the average current is \[ I = \frac{Q}{t} = \frac{20000}{10} = 2000\text{ A} \]
Step 2: Find the electrical power delivered.
With a potential difference of $V = 10\text{ V}$ driving this current, the power is \[ P = VI = 10 \times 2000 = 20000\text{ W} \]
Step 3: Convert power over time into total work done.
Work done is just power multiplied by the time for which it acts, \[ W = P \times t = 20000 \times 10 = 200000\text{ J} \]
Step 4: Write this in scientific notation.
$200000\text{ J}$ is the same as $2 \times 10^5$ joules, and the resistance value given was not even needed for this calculation.
\[ \boxed{2 \times 10^5\text{ J}} \]