Final answer:
To find how long it takes a 10-mA current to charge a capacitor with 5.0 mC, use the relation I = Q / t, rearrange for t, which gives t = Q / I, and substitute the values to find t = 0.50 s.
Step-by-step explanation:
The question is asking how long it would take for a 10-mA (milliampere) current to charge a capacitor with a charge of 5.0 mC (millicoulombs). To solve this, we can use the relationship between current (I), charge (Q), and time (t), which is given by the equation I = Q / t. Substituting the given values into this equation allows us to solve for the time t.
First, convert the current into amperes: 10 mA = 10 × 10⁻³ A = 0.01 A. Then rearrange the equation to solve for time t: t = Q / I. Finally, substitute the values: t = 5.0 mC / 0.01 A = 5.0 × 10⁻³ C / 0.01 A = 0.50 s. So, the correct answer to the question is (a) 0.50 s.