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We have to measure the voltage across a-b in this circuit with an analog oscilloscope, but neither of these points are grounded. How should we put the channels of oscilloscope to perform the measurement?

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Put the ground clips of two scope probes on the ground of the circuit (the one denoted with ground symbol). Then put Channel A on point A, channel B on point B, and then use the Math function of the scope to display the difference between two signals.

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    \$\begingroup\$ Why can't you put the ground pin on B and the probe on A - just like it would be done with a multimeter? \$\endgroup\$ – Mike Spark Nov 18 '14 at 16:07
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    \$\begingroup\$ @MikeSpark - because a multimeter is floating and "isolated". If you clip the scope ground to B then you're probably shorting out R2 through your scope. \$\endgroup\$ – brhans Nov 18 '14 at 16:11
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    \$\begingroup\$ @MikeSpark The oscilloscope's ground is most likely a single common point between all of the probes an it COULD be the same ground as a power power supply of the circuit. Now imagine what will happen when you connect the power supply's ground to one of the points. \$\endgroup\$ – Eugene Sh. Nov 18 '14 at 16:12
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    \$\begingroup\$ Because the scope probe ground should be at the same potential as the earth ground. If the circuit is also connected to earth ground, then your scope probe ground will short your circuit to ground at a point it wasn't designed for - incorrect measurment guaranteed, possible sparks and "kaboom" depending on C1 and the amount of current that Vs can deliver. \$\endgroup\$ – JRE Nov 18 '14 at 16:12
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    \$\begingroup\$ @JamieHanrahan But who said they want the RMS? Sometimes the complex wave is the desired output. \$\endgroup\$ – Eugene Sh. Nov 18 '14 at 21:28

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