Final answer:
Without a voltmeter, the voltage across the 10-kΩ resistor is 100 V, while with a 200-kΩ voltmeter in parallel, the voltage is reduced to 98.4 V. Ammeters are designed to have very low resistance and are placed in series with a component without significantly affecting the current in the circuit.
Step-by-step explanation:
To determine the voltage across the 10-kΩ resistor without the voltmeter connected, we can use Ohm's law and the series circuit rules. In a series circuit, the total resistance is the sum of individual resistances, which is 5 kΩ + 10 kΩ = 15 kΩ. The total current in the circuit is found using Ohm's law (I = V/R), so I = 150 V / 15 kΩ = 0.01 A (10 mA). The voltage across the 10-kΩ resistor is then V = I * R = 10 mA * 10 kΩ = 100 V.
Now, with the voltmeter connected across the 10-kΩ resistor, the voltmeter's resistance comes into play. The effective resistance across the 10-kΩ resistor and the 200-kΩ voltmeter in parallel is found using the formula 1/Req = 1/R1 + 1/R2, which gives us Req = 9.8 kΩ. The current through the 10-kΩ branch is now I = 150 V / (5 kΩ + 9.8 kΩ) = 0.00984 A (9.84 mA). The voltage across the 10-kΩ resistor (and voltmeter) is V = I * Req = 9.84 mA * 9.8 kΩ = 98.4 V
When measuring current with an ammeter, the instrument needs to be placed in series with the circuit element. Because ammeters have very low resistance to minimize their effect on circuit measurements, they should not significantly alter the total resistance of the circuit. However, even a small resistance added to a circuit can change the current slightly, especially in low resistance paths.