Root mean square values and oscilloscopes

The diagram shows an ac signal displayed on an oscilloscope screen.

The time base is set to 5 μs div⁻¹.

What is the frequency of the signal?

This question is based on an investigation into how the frequency of the first-harmonic stationary wave on a string varies with tension (required practical activity 1).

Figure 1 shows the arrangement for this investigation.

The tension in the string is equal to the weight mg of the total mass m tied to the string.

The frequency is changed until the first-harmonic stationary wave appears on the string. This frequency f is determined using the oscilloscope.

The process is repeated for different values of m.

Identify two control variables for the arrangement shown in Figure 1.

You may annotate Figure 1 as part of your answer.

The total mass m is made from a mass hanger and up to three slotted masses.

One 20 g, one 50 g and one 100 g slotted mass are provided. The hanger has a mass of 100 g.

The hanger must not be removed from the string.

Which statement is correct?

Tick (✓) one box.

The frequency f is calculated using the waveform displayed on the oscilloscope. Figure 2 shows the waveforms displayed on the oscilloscope when m = 100 g and when m = 200 g.

m = 100 g m = 200 g

The y-voltage gain setting is 5 V div⁻¹. The time-base setting is 20 ms div⁻¹.

Determine V_rms, the root mean square voltage of the ac supply.

Determine the period of the waveform on Figure 2 when m = 100 g.

Deduce whether Figure 2 shows the expected result of doubling m from 100 g to 200 g.

A signal generator supplies a sinusoidal root mean square voltage of 7.0 V. The sinusoidal voltage is displayed on an oscilloscope screen. The screen has eight vertical divisions.

Which volts/division setting will display the tallest complete waveform?

Two signals that have the same frequency are displayed simultaneously on an oscilloscope. The display is shown with the time-base set to 5 ms div⁻¹.

Which row shows the frequency of both signals and the phase difference between them?

Power P is dissipated in a resistor of resistance R carrying a direct current I.

A second resistor of resistance 2 R carries an alternating current with peak value I.

What is the power dissipated in the second resistor?

Figure 1 shows apparatus used to measure the speed of sound in a steel rod.

The steel rod is suspended from a beam using rubber bands. When the hammer is in contact with the end L of the steel rod, a circuit is completed and the signal generator is connected to the oscilloscope.

Figure 2 shows the waveform then displayed on the oscilloscope.

Which control on the oscilloscope should be used to centre the trace vertically on the screen? Tick (✓) one box.

When the hammer hits end L, a sound wave travels along the steel rod and is reflected at end R. When the wave returns to L the rod bounces away from the hammer and the circuit is broken.

Figure 3 shows the waveform produced by the brief contact between the hammer and L. Note that the waveform has now been centred vertically.

Figure 4 shows the time-base setting of the oscilloscope.

The distance between L and R in Figure 1 is 0.870 m.

Deduce the speed of sound in the steel rod.

A student repeats the experiment using a steel rod of twice the length.

Explain:

• how using the longer rod affects the waveform displayed

• any changes needed to get an accurate result for the speed.

You should include numerical detail.

Mains electricity is rated 230 V in the UK.

Which is correct?

In a resistor of resistance R, a steady current I dissipates a power P. In a resistor of resistance there is an alternating current of root mean square value 3I. What is the mean power dissipated in the resistor of resistance ?

Figure 6 shows an oscilloscope connected across resistor R which is in series with an ac supply. The supply provides a sinusoidal output of peak voltage 15 V.

Calculate the rms voltage of the supply.

Figure 7 shows the trace of the waveform displayed on the oscilloscope.

Determine the y-voltage gain of the oscilloscope used for Figure 7.

A dc supply gives the same rate of energy dissipation in R as the ac supply in Figure 6.

Draw the trace of the output of the dc supply on Figure 7. The oscilloscope settings remain the same.

The ac supply shown in Figure 6 is replaced with a square-wave generator operating between 0 and +15 V.

Figure 8 shows the trace of the new waveform displayed on the oscilloscope. The time-base is set to 5.0 × 10⁻⁴ s div⁻¹.

Calculate the frequency of the square waves.

Figure 9 shows the arrangement with the square-wave generator connected to an RC circuit. A capacitor C is placed in series with the resistor R. The oscilloscope is connected across the capacitor C.

The capacitor charges and discharges.

Figure 10 shows the trace of the waveform displayed on the oscilloscope. The settings of the oscilloscope remain the same as in Question 04.4.

Deduce the time constant for the RC circuit, explaining each step of your method.

State and explain a change to one control setting on the oscilloscope that would reduce the uncertainty in the value of the time constant.

A steady current I dissipates power P in a resistor of resistance R. An alternating current through a resistor of resistance 2 R has a peak value of I.

What is the power dissipated in the second resistor?

The figure shows an oscilloscope trace of a sinusoidal ac voltage.

The time base setting is 5 ms cm^–1 and the Y-voltage gain is 10 V cm^–1.

Which row describes the ac voltage?

A stationary wave is formed on a stretched wire.

Figure 14 shows the wire, fixed at one end, supported by two bridges and passing over a pulley.

A 0.500 kg mass is attached to the free end of the wire. A uniform horizontal magnetic field is applied perpendicular to the wire between the bridges. A signal generator is connected to each end of the wire.

The oscilloscope shown is used to determine the frequency of the output of the signal generator. The wire oscillates because the alternating current in the wire interacts with the magnetic field.

Figure 15 shows the first harmonic stationary wave produced when the distance x between the bridges is adjusted.

The output potential difference (pd) of the signal generator is displayed on the oscilloscope, as shown in Figure 16.

The time-base setting of the oscilloscope is 10 ms cm¹.

Determine f, the frequency of the alternating pd.

A metre ruler is placed next to the bridges supporting the wire, as shown in Figure 17

Determine c.

Determine, in kg m¹, the mass per unit length of the wire.

A student uses digital vernier callipers to measure the diameter of a cylindrical metal rod. The student places the rod between the jaws of the callipers and records the reading indicated. Without pressing the zero button, the student removes the rod and closes the jaws.

Figure 18 shows the calliper readings in millimetres, before and after the jaws are closed.

Calculate the diameter d of the rod.

Describe relevant procedures to limit the effect of random error in the result for d.

Determine the density of the rod. The mass per unit length of the rod is 3.54 10³ kg m¹.

What is the peak current in the resistor?

What is the peak power dissipated in the lamp?

The Y-voltage gain and time-base settings of the oscilloscope are shown in Figure 6.

When switch S is open (off) the oscilloscope displays the waveform shown in Figure 7.

When S is closed (on) the oscilloscope displays the waveform shown in Figure 8.

Determine the peak-to-peak voltage V of the waveform shown in Figure 8.

Determine the frequency f of the waveform shown in Figure 8.

Figure 9 shows the signal generator connected in series with a resistor R and a capacitor C.

The oscilloscope is connected across the capacitor. The Y-voltage gain and time-base settings are still the same as shown in Figure 6.

When S is closed (on) the oscilloscope displays the waveform shown in Figure 10.

Determine the time constant of the circuit in Figure 9.

A student suggests that setting the time-base to 0.2 ms division might reduce uncertainty in the determination of the time constant.

State and explain any possible advantage or disadvantage in making this suggested adjustment.

The student connects an identical resistor in parallel with R and uses the oscilloscope to display the waveform across C.

Draw on Figure 11 the waveform you expect the student to see.

The waveform of Figure 10 is shown as a dashed line to help you show how the waveform changes.

Explain the change in the waveform.

Figure 12a is a graph of voltage against time showing the output of the signal generator. Figure 12b shows the voltage across C during the same time interval. The student interchanges the positions of R and C and connects the oscilloscope across R. Complete Figure 12c to draw the voltage across R during the time interval.

State and explain what changes, if any, the student needs to make to the settings of the oscilloscope so the waveform across R is fully displayed.