Question: 23 A heater is connected in series with a dc power supply, a variable resistor and an ammeter in the circuit shown.
The variable resistor is adjusted until the reading on the ammeter is $0.50A$ and the resistance of the heater is $8.0\Omega$.
How much energy is converted to thermal energy in $5.0$ minutes?
A $10J$
B $40J$
C $160J$
D $600J$
E $2400J$
F $9600J$
1. **Problem Statement:**
A heater with resistance $8.0\Omega$ is connected in series with a variable resistor and a DC power supply. The current through the circuit is $0.50A$. We want to find the thermal energy converted in $5.0$ minutes.
2. **Relevant Formula:**
The thermal energy converted by a resistor is given by the electrical power dissipated multiplied by time:
$$E = P \times t$$
where power $P$ is:
$$P = I^2 R$$
and $I$ is current, $R$ is resistance, $t$ is time.
3. **Calculate power dissipated by the heater:**
$$P = (0.50)^2 \times 8.0 = 0.25 \times 8.0 = 2.0\text{ watts}$$
4. **Convert time to seconds:**
$$5.0\text{ minutes} = 5.0 \times 60 = 300\text{ seconds}$$
5. **Calculate energy converted:**
$$E = P \times t = 2.0 \times 300 = 600\text{ joules}$$
6. **Answer:**
The energy converted to thermal energy in $5.0$ minutes is $600J$, which corresponds to option D.