Final answer:
a. The resistance of the combination is 74.5 kΩ. b. The percent increase in current through the combination is 0%. c. The percentage decrease in voltage across the combination cannot be calculated without the values of voltage and current.
Step-by-step explanation:
a. The resistance of the combination can be calculated using the formula for resistors in parallel, which is given by:
1/R_total = 1/R_1 + 1/R_2 + ... + 1/R_n
where R_total is the total resistance and R_1, R_2, ..., R_n are the resistances of the individual components.
In this case, the combination consists of the 74.5-kΩ resistor and the 1.25-MΩ voltmeter. Plugging in the values:
1/R_total = 1/74.5k + 1/1.25M = 13.4 x 10^-6
Therefore, the resistance of the combination is:
R_total = 74.5kΩ || 1.25MΩ = 1/(13.4 x 10^-6) = 74.5kΩ
b. The current through a resistor is given by Ohm's Law: I = V/R, where I is the current, V is the voltage, and R is the resistance. In this case, the voltage across the combination is kept the same as it was across the 74.5-kΩ resistor alone. Therefore, the current through the combination would be:
I_combination = V/R_combination = V/74.5kΩ
The percentage increase in current can be calculated by comparing the current through the combination to the current through the 74.5-kΩ resistor alone:
Percentage increase = ((I_combination - I_resistor alone)/I_resistor alone) x 100
Substituting the values:
Percentage increase = ((V/74.5kΩ - V/74.5kΩ)/V/74.5kΩ) x 100 = 0%
c. To keep the current through the combination the same as it was through the 74.5-kΩ resistor alone, the voltage across the combination needs to change. The voltage across a resistor can be calculated using Ohm's Law: V = I*R, where V is the voltage, I is the current, and R is the resistance. In this case, the current through the combination is kept the same as it was through the 74.5-kΩ resistor alone. Therefore, the voltage across the combination would be:
V_combination = I_resistor alone x R_combination = I_resistor alone x 74.5kΩ
The percentage decrease in voltage can be calculated by comparing the voltage across the combination to the voltage across the 74.5-kΩ resistor alone:
Percentage decrease = ((V_resistor alone - V_combination)/V_resistor alone) x 100
Substituting the values:
Percentage decrease = ((V_resistor alone - I_resistor alone x 74.5kΩ)/V_resistor alone) x 100
However, the values for the voltage and current are not given in the question, so it is not possible to calculate the percentage decrease in voltage.