To find out how long current 2 (10.5 A) needs to run to deliver the same amount of charge as current 1 (8.4 A) did in 240 seconds, we first calculate the charge delivered by current 1.
The charge \( Q \) is given by the formula:
\[ Q = I \times t \]
where \( I \) is the current and \( t \) is the time.
For current 1: \[ Q_1 = 8.4 , \text{A} \times 240 , \text{s} = 2016 , \text{C} \]
Now we need to find the time \( t_2 \) that current 2 has to run to deliver the same charge of 2016 C.
For current 2: \[ Q_2 = 10.5 , \text{A} \times t_2 \]
Setting \( Q_1 \) equal to \( Q_2 \): \[ 2016 , \text{C} = 10.5 , \text{A} \times t_2 \]
Now we can solve for \( t_2 \): \[ t_2 = \frac{2016 , \text{C}}{10.5 , \text{A}} \approx 192 , \text{s} \]
Thus, current 2 needs to run for approximately 192 seconds to deliver the same amount of charge as current 1 did.
So, the answer is: 192 s.
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