Of course, I'd be happy to help you solve this problem!
Given:
- Voltage ([tex]\(V\)[/tex]) = 230 volts
- Energy transferred per second = 96 joules
First, recall that power ([tex]\(P\)[/tex]) is the rate at which energy is transferred. In this case, since energy is given per second, the power is equal to the energy value:
[tex]\[ P = \frac{E}{t} \][/tex]
where:
- [tex]\( P \)[/tex] is power in watts (W)
- [tex]\( E \)[/tex] is energy in joules (J)
- [tex]\( t \)[/tex] is time in seconds (s)
Since the energy transferred per second is already given as 96 J, this means:
[tex]\[ P = 96 \text{ watts} \][/tex]
Next, we use the relationship between power, voltage, and current, which is given by the formula:
[tex]\[ P = V \times I \][/tex]
where:
- [tex]\( I \)[/tex] is current in amperes (A)
- [tex]\( V \)[/tex] is voltage in volts (V)
We can rearrange the formula to solve for the current ([tex]\(I\)[/tex]):
[tex]\[ I = \frac{P}{V} \][/tex]
Substitute the given values into the equation:
[tex]\[ I = \frac{96 \text{ W}}{230 \text{ V}} \][/tex]
Perform the division:
[tex]\[ I \approx 0.4174 \text{ A} \][/tex]
Finally, we round the result to 1 decimal place:
[tex]\[ I \approx 0.4 \text{ A} \][/tex]
So, the current through the lamp is approximately [tex]\( 0.4 \)[/tex] amperes.
