23P2Q05

5a)

The graph starts off as a straight line passing through the origin, and then becomes a steepening curve.

Since resistance is the voltage to current ratio, the graph is showing that resistance of the thermistor is constant at low V values, but decreases with V when V is large.

5bi)

The current through both resistors are the same.

\displaystyle \frac{{{P}_{220}}}{{{P}_{640}}}=\frac{{{I}^{2}}{{R}_{220}}}{{{I}^{2}}{{R}_{640}}}=\frac{220}{640}=0.34

5bii)

No effect.

While the current drawn from the supply is now lower, both resistors still carry the same current.

The ratio in (b)(i) depends only on the ratio of the resistances.

5biii)

Total resistance in series:       \displaystyle {{R}_{s}}=220+640=860\text{  }\Omega \text{ }

Total resistance in parallel:     \displaystyle {{R}_{p}}={{(\frac{1}{220}+\frac{1}{640})}^{-1}}=163.7\text{  }\Omega\text{ }

\displaystyle \frac{{{I}_{s}}}{{{I}_{p}}}=\frac{\varepsilon }{{{R}_{s}}}\div \frac{\varepsilon }{{{R}_{p}}}=\frac{{{R}_{p}}}{{{R}_{s}}}=\frac{163.7}{860}=0.190

5biv)

No effect.

Since both the series and parallel circuits are connected to the same a.c. power supply with the same peak voltages, the ratio of the peak (or rms) currents depends only on ratio of the resistances.

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