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$1.$What happens when a resistor of very high resistance (say $10,000 \Omega $) is connected in parallel with a resistor of comparatively lower resistance of about (say $100 \Omega $)?

Is the overall resistance going to be lesser than $100 \Omega $?

And how to calculate the voltage across the the net resistance of above resistors in parallel?

$2.$ What exactly happens when an infinite resistance is connected across a circuit?

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  • $\begingroup$ Yes the res is a tiny bit lower than 100. Voltage is the same in parallel. An infinite resistance has no effect, like air, so small it's hard to measure. $\endgroup$ – PhysicsDave Apr 16 at 3:50
  • $\begingroup$ Use air as your infinite resistance resistor for all your high school electric circuits. Now I think you can answer yourself. $\endgroup$ – user8718165 Apr 16 at 4:13
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When 2 resistors are connected in parallel, the resulting total resistance is given by $$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$$

From that you can see that, if a very large resistance $R_2$ is put in parallel with $R_1$, the total resistance changes very little (because if $R_2$ is very large, $1/R_2$ is very small

Alternatively, if we rework the equation to become $$R=\frac{R_1 * R_2}{R_1+R_2}$$ you can see that, for $R_1=100$ and $R_2=10000$ we have $$R=100*10000/10100=99.0099$$ so the change is quite small. The larger $R_2$ the smaller the change.

As for the voltage across the 2 resistors, this is given by the current through the resistor multiplied by the resistance. In this case, the resistance changes very little, so does the current, and the voltage changes only minimally. To determine exactly what happens you need more details, such as the rest of the circuit, the current the battery can supply, and the internal resistance of the battery

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What happens when a resistor of very high resistance (say 10,000 ohms) is connected parallelly with a resistor of comparatively lower resistance (about 100 ohms)?

Current flows through each resistor according to Ohm's Law. If you apply a voltage $V$, then the current through a resistor is $I=V/R$.

Is the overall resistance going to be lesser than 100 ohms

Adding additional resistors in parallel to an existing resistor network always reduces the equivalent resistance.

How to calculate the voltage across the the resultant resistance of above resistors in parallel?

It depends on the complete circuit they're connected to.

what exactly happens when an infinite resistance is connected across a circuit?

An infinite resistance is an open circuit. Just like the air that already surrounds your circuit.

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