Before starting with the problem, let's remind that:
- Total resistance of a combination of resistors in series is:
- Total resistance of a combination of resistors in parallel is given by:
Now let's apply these equations to solve the different parts of the problem:
1. All the resistors in series:
In this case, the total resistance is
2. All the resistors are connected in parallel:
In this case, the total resistance is
3. The 6.50 Ω and 7.60 Ω resistors are connected in parallel, and the 1.70-Ω resistor is connected in series with the parallel combination:
The total resistance of the two resistors connected in parallel is
And the combination of these with the other resistor of 1.70-Ω in series gives a total resistance of
4. The 6.50 Ω and 1.70 Ω resistors are connected in parallel, and the 7.60-Ω resistor is connected in series with the parallel combination:
The total resistance of the two resistors connected in parallel is
And the combination of these with the other resistor of 7.60-Ω in series gives a total resistance of
5. The 7.60 Ω and 1.70 Ω resistors are connected in parallel, and the 6.50-Ω resistor is connected in series with the parallel combination:
The total resistance of the two resistors connected in parallel is
And the combination of these with the other resistor of 6.50-Ω in series gives a total resistance of
6. The 6.50 Ω and 7.60 Ω resistors are connected in series, and the 1.70-Ω resistor is connected in parallel with the series combination:
In this case, the total resistance of the two resistors in series is
And the combination of these with the other resistor of 1.70-Ω in parallel gives a total resistance of
7. The 6.50 Ω and 1.70 Ω resistors are connected in series, and the 7.60-Ω resistor is connected in parallel with the series combination:
In this case, the total resistance of the two resistors in series is
And the combination of these with the other resistor of 7.60-Ω in parallel gives a total resistance of
8. The 7.60 Ω and 1.70 Ω resistors are connected in series, and the 6.50-Ω resistor is connected in parallel with the series combination:
In this case, the total resistance of the two resistors in series is
And the combination of these with the other resistor of 6.50-Ω in parallel gives a total resistance of