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The equivalent resistance of n resistors connected in parallel is given by
(1)
In our problem, the resulting resistance of the 5 pieces connected in parallel is
, and since the 5 pieces are identical, their resistance R is identical, so we can rewrite (1) as
From which we find
.
So, each piece of wire has a resistance of
. Before the wire was cut, the five pieces were connected as they were in series. The equivalent resistance of a series of n resistors is given by
So if we apply it at our case, we have
therefore, the resistance of the original wire was
.
In our problem, the resulting resistance of the 5 pieces connected in parallel is
From which we find
So, each piece of wire has a resistance of
So if we apply it at our case, we have
therefore, the resistance of the original wire was
1) Let's start by calculating the equivalent resistance of the three resistors in parallel, 
:
From which we find
Now all the resistors are in series, so the equivalent resistance of the circuit is the sum of all the resistances:
So, the correct answer is D)
2) Let's start by calculating the equivalent resistance of the two resistors in parallel:
From which we find
And these are connected in series with a resistor of, so the equivalent resistance of the circuit is
And by using Ohm's law we find the current in the circuit:
So, the correct answer is C).
3) Let' start by calculating the equivalent resistance of the two resistors in parallel:
From which we find
Then these are in series with all the other resistors, so the equivalent resistance of the circuit is
And by using Ohm's law we find the current flowing in the circuit:
And so the voltage read by the voltmeter V1 is the voltage drop across the resistor 2-3:
So, the correct answer is D).
4) Again, let's start by calculating the equivalent resistance of the two resistors in parallel:
From which we find
Now all the resistors are in series, so the equivalent resistance of the circuit is:
The current in the circuit is given by Ohm's law
Now we can compare the voltage drops across the resistors. Resistor 1:
Resistor 2 and resistor 3 are in parallel, so they have the same voltage drop:
Resistor 4:
So, the greatest voltage drop is on resistor 1, so the correct answer is D).
5) the figure shows a circuit with a resistor R and a capacitor C, so it is an example of RC circuit. Therefore, the correct answer is D).
6) The circuit is the same as part 4), so the calculations are exactly the same. Therefore, the power dissipated on resistor 3 is
So, correct answer is B).
7) The circuit is the same as part 4), so we can use exactly the same calculation, and we immediately see that the resistor with lowest voltage drop was R4 (2.50 V), so the correct answer is B) R4.
From which we find
Now all the resistors are in series, so the equivalent resistance of the circuit is the sum of all the resistances:
So, the correct answer is D)
2) Let's start by calculating the equivalent resistance of the two resistors in parallel:
From which we find
And these are connected in series with a resistor of
And by using Ohm's law we find the current in the circuit:
So, the correct answer is C).
3) Let' start by calculating the equivalent resistance of the two resistors in parallel:
From which we find
Then these are in series with all the other resistors, so the equivalent resistance of the circuit is
And by using Ohm's law we find the current flowing in the circuit:
And so the voltage read by the voltmeter V1 is the voltage drop across the resistor 2-3:
So, the correct answer is D).
4) Again, let's start by calculating the equivalent resistance of the two resistors in parallel:
From which we find
Now all the resistors are in series, so the equivalent resistance of the circuit is:
The current in the circuit is given by Ohm's law
Now we can compare the voltage drops across the resistors. Resistor 1:
Resistor 2 and resistor 3 are in parallel, so they have the same voltage drop:
Resistor 4:
So, the greatest voltage drop is on resistor 1, so the correct answer is D).
5) the figure shows a circuit with a resistor R and a capacitor C, so it is an example of RC circuit. Therefore, the correct answer is D).
6) The circuit is the same as part 4), so the calculations are exactly the same. Therefore, the power dissipated on resistor 3 is
So, correct answer is B).
7) The circuit is the same as part 4), so we can use exactly the same calculation, and we immediately see that the resistor with lowest voltage drop was R4 (2.50 V), so the correct answer is B) R4.