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I have learnt about an experiment to demonstrate Faraday's law using the setup below. In the experiment a solenoid is connected across a signal generator, whose frequency can be altered, and a search coil is placed at the centre of the solenoid (perpendicular to the B-field). As the AC flows through the solenoid, a changing magnetic field is created through the solenoid creating an ever changing flux-linkage through the search coil ∴ inducing an ever changing emf across the search coil. You can then show the relationship between emf and flux linkage by changing the frequency of the supply or adjusting the resistance of the variable resistor. enter image description here

I am just wondering if it is possible to demonstrate Faraday's law using the relationship between the back emf created through the solenoid by self induction. I'm a bit stuck on how this would work though (the diagram below shows one idea but I don't think the voltmeter would measure the back emf so it wouldn't work). enter image description here

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What you showed here is an RL circuit and what you measure in this way is $L\frac{di}{dt}$ or $\epsilon(t)-Ri(t)$.

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