Many resistors connected in series will?a)Divide the voltage proportio...
In a series circuit, the current remains the same across all resistors hence the voltage divides proportionally among all resistors.
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Many resistors connected in series will?a)Divide the voltage proportio...
C:
Increase the source voltage in proportion to the values of the resistors
Many resistors connected in series will?a)Divide the voltage proportio...
Series Connection of Resistors
When resistors are connected in series, they are arranged sequentially, with one resistor connected to the terminal of another resistor, forming a single path for current flow. In this configuration, the current passing through each resistor is the same and equal to the total current flowing through the series circuit.
Dividing Voltage Proportionally
When resistors are connected in series, the voltage across the entire series combination is equal to the sum of the individual voltages across each resistor. According to Ohm's law (V = IR), the voltage drop across a resistor is directly proportional to its resistance.
Since the current is the same throughout the series circuit, the voltage drop across each resistor is proportional to its resistance. This means that resistors with higher resistance will have a higher voltage drop, while resistors with lower resistance will have a lower voltage drop. Therefore, when resistors are connected in series, the voltage is divided proportionally among all the resistors.
Example:
Let's consider a simple example to illustrate this concept. Suppose we have three resistors connected in series, with resistances of 2 ohms, 4 ohms, and 6 ohms, respectively. If a 12-volt potential difference is applied across the series combination, we can calculate the voltage drop across each resistor as follows:
- The total resistance in the series combination is 2 + 4 + 6 = 12 ohms.
- The total current flowing through the series circuit can be calculated using Ohm's law: I = V/R = 12V / 12Ω = 1A.
- The voltage drop across each resistor can be determined using Ohm's law: V = IR.
- For the 2-ohm resistor: V1 = 1A * 2Ω = 2V.
- For the 4-ohm resistor: V2 = 1A * 4Ω = 4V.
- For the 6-ohm resistor: V3 = 1A * 6Ω = 6V.
As we can see, the voltage drop across each resistor is proportional to its resistance. The 2-ohm resistor has a voltage drop of 2 volts, the 4-ohm resistor has a voltage drop of 4 volts, and the 6-ohm resistor has a voltage drop of 6 volts. The total voltage drop across the series combination is equal to the sum of the individual voltage drops: 2V + 4V + 6V = 12V, which matches the applied potential difference.
Therefore, when resistors are connected in series, the voltage is divided proportionally among all the resistors.
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