Two scales on a voltmeter measure voltages up to 20.0 V and 27.0 V, respectively. The resistance connected in series with the galvanometer is 1680 Ù for the 20.0-V scale and 2930 Ù for the 27.0-V scale.
Well, it seems like these scales are competing to see who can measure the highest voltage! It's like a game of "Who can reach the highest number?" But don't worry, I'm here to help you understand what's going on.
When you connect a resistance in series with a galvanometer, it forms what we call a voltmeter. It helps us measure voltage accurately. The resistance values you mentioned, 1680 Ω and 2930 Ω, are the ones connected in series with the galvanometers for the respective scales.
Now, let's talk about the scales themselves. The first scale measures voltages up to 20.0 V, and the second scale goes up to 27.0 V. It's like one scale is aiming for greatness, but the other one wants to go even higher! I guess you could say they have a little friendly competition.
By having different resistances connected in series, these scales offer different ranges. The greater the resistance, the higher the range of voltage you can measure. So, the 20.0-V scale has a lower resistance, which limits the range to 20.0 V. On the other hand, the 27.0-V scale has a higher resistance, allowing it to measure up to 27.0 V.
In summary, the different resistance values connected in series with the galvanometers create different scales that can measure different ranges of voltage. It's like having different superheroes with different superpowers – one can measure up to 20.0 V, while the other one can go up to 27.0 V.
To calculate the voltage measured on each scale, we need to apply Ohm's law, which states that voltage is equal to the product of current and resistance.
For the 20.0 V scale:
Resistance (R) = 1680 Ω
Voltage (V) = 20.0 V
Using Ohm's law:
V = I * R
Rearranging the equation to solve for current (I):
I = V / R
Plugging in the values:
I = 20.0 V / 1680 Ω
I ≈ 0.0119 A
The current passing through the circuit is approximately 0.0119 A.
Now, let's calculate the voltage using the 27.0 V scale:
Resistance (R) = 2930 Ω
Voltage (V) = 27.0 V
Using Ohm's law:
V = I * R
Using the previously calculated current (I):
V = 0.0119 A * 2930 Ω
V ≈ 34.93 V
Therefore, the voltage measured on the 27.0 V scale is approximately 34.93 V.
To understand the use of scales on a voltmeter and the role of resistance, let's break down the information provided:
1. Voltmeter Scales:
The voltmeter has two scales:
a) 20.0 V scale: This scale measures voltages up to 20.0 volts.
b) 27.0 V scale: This scale measures voltages up to 27.0 volts.
2. Resistance:
The resistance connected in series with the galvanometer (which is the part that detects and measures the voltage) is given:
a) For the 20.0 V scale: The resistance is 1680 ohms (Ù).
b) For the 27.0 V scale: The resistance is 2930 ohms (Ù).
Now, let's explain how the voltmeter works and how the resistance affects the measurements:
A voltmeter is an instrument used to measure voltage. It is connected in parallel to the component or circuit whose voltage we want to measure. When connected in parallel, the voltmeter obtains a voltage reading proportional to the voltage across the measured component.
To ensure that the voltmeter does not significantly affect the circuit being measured, a high resistance (known as the "multiplier" or "series resistance") is connected in series with the galvanometer (the main component of the voltmeter). This allows the voltmeter to draw very little current from the circuit under test.
The resistance is carefully chosen so that the voltage dropped across it is proportional to the range of the voltmeter scale. This allows the voltmeter to measure different voltage ranges accurately.
In this case, we have two scales with different resistance values. The 20.0 V scale has a higher resistance (1680 Ù) compared to the 27.0 V scale (2930 Ù). This means that for the same voltage applied to the voltmeter, a smaller proportion of the voltage will be dropped across the galvanometer in the 20.0 V scale, compared to the 27.0 V scale.
By adjusting the resistance value, the voltmeter ensures that the voltage range it measures falls within the maximum limit specified for each scale. This prevents the galvanometer from being damaged by higher voltages.
To summarize, the two scales on the voltmeter allow for different voltage ranges to be measured accurately. The use of different resistance values helps protect the galvanometer and ensures that the voltage reading falls within the desired range for each scale.