A thermistor is connected in series with a 600 Ω fixed resistor and a 6.0 V battery of negligible internal resistance. The table shows how the resistance of...
Question 1 Report
A thermistor is connected in series with a 600 Ω fixed resistor and a 6.0 V battery of negligible internal resistance. The table shows how the resistance of the thermistor varies with temperature.
| Temperature / °C | Thermistor resistance / Ω |
|---|---|
| 10 | 5400 |
| 20 | 2400 |
| 30 | 600 |
| 40 | 200 |
At which temperature is the potential difference across the fixed resistor equal to 3.0 V?
Answer Details
The potential difference across the fixed resistor is:
\[ V_{\text{fixed}} = V_{\text{supply}} \times \frac{R_{\text{fixed}}}{R_{\text{therm}} + R_{\text{fixed}}} \]For \( V_{\text{fixed}} = 3.0 \) V:
\[ 3.0 = 6.0 \times \frac{600}{R_{\text{therm}} + 600} \]\[ \frac{R_{\text{therm}} + 600}{600} = \frac{6.0}{3.0} = 2.0 \]\[ R_{\text{therm}} + 600 = 1200 \]\[ R_{\text{therm}} = 600 \text{ } \Omega \]From the table, the thermistor has a resistance of 600 \(\Omega\) at 30 \(^\circ\)C. When the thermistor and fixed resistor are equal, the supply voltage is shared equally.
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