Root mean square values & oscilloscopes

The potential difference (p.d.) from a power pack alternates at a frequency of 50 Hz. The root-mean-square (r.m.s.) value of the output p.d. is measured to be 8.5 V using an a.c. voltmeter.

The output from the power pack is connected to a resistor of resistance 1.5 Ω.

Show that the rate of power dissipation in the resistor is about 48 W.

A lab technician used the resistor to heat 1.25 10^–4m³ of milk in a beaker.

Calculate the time taken for the milk to increase in temperature by 12 °C.

specific heat capacity of milk = 3930 J kg^–1K^–1

The lab technician used an oscilloscope to determine the supply frequency and check the r.m.s. output p.d. displayed by the voltmeter.

Describe the methods the technician should use.

The circuit shows a 1 mF capacitor connected to an a.c. supply. The graph shows how the potential difference V varies with time t.

Calculate the root‑mean‑square potential difference.

The formula used to generate this graph is V = 5 sin (100 πt)

Explain why this formula leads to the graph above.

A spreadsheet is used to model how the current I in the 1 mF capacitor varies with t. Six rows of the spreadsheet are shown below.

Explain how cell E10 has been calculated.

State the formula used to calculate cell G11.

Calculate the maximum energy stored on the capacitor.

The spreadsheet data are used to plot a graph to show how I varies with t. This is shown as a dashed line below.

The corresponding graph of V against t is also shown as a continuous line.

Deduce whether the capacitor dissipates power over one cycle of the a.c. supply.

Power supplies provide either alternating or direct currents and potential differences.

A power supply produces an alternating potential difference (p.d.). The p.d. has a period of 0.02 s and a peak value of 4.0 V.

Calculate the frequency of the supply.

Calculate the root‑mean‑square p.d.

Root‑mean‑square p.d. =_........

It is possible to convert alternating currents and p.d.s, to direct currents and p.d.s using diodes.

The power supply provides an input V_in to the circuit shown. The circuit includes four diodes D₁, D₂, D₃ and D₄ and a resistor R. The circuit produces an output

A graph of V_in against time and a corresponding graph of V_out against time are shown below.

Explain the operation of this circuit. Your answer should refer to D₁, D₂, D₃ and D₄.

A capacitor is added between points X and Y in the circuit.

The new graph of V_out against time is shown below.

Determine a value for the capacitance of the capacitor.

resistance of R = 2.2 kΩ

A student connected the output from a source of alternating potential difference (p.d.) to a series resistor combination.

She connected an oscilloscope across the 150 Ω resistor as shown.

The trace obtained on the oscilloscope is shown below.

Determine the peak p.d. across the 150 Ω resistor.

y-sensitivity of oscilloscope = 2.0 V per division

Peak p.d. across 150 Ω resistor =_........

Calculate the root mean square (r.m.s.) value of the current in the circuit.

r.m.s. value of current =_........

Calculate the power dissipated in the circuit.

Another student suggested that a voltmeter would be more accurate than using an oscilloscope to determine the magnitude of the p.d.

Comment on this suggestion.

A wire carries an alternating current of peak value 3 A.

Which of the following is the root-mean-square value of this current?