4.3.3 Action and use of circuit components (3)
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1.
A potential divider circuit is designed to provide a voltage of 6V from a 15V power supply. Two resistors are used. One resistor has a value of 3kΩ. Calculate the value of the second resistor required. Show your working.
The potential divider equation is: V1 / V2 = R1 / R2
We are given V1 = 6V, V2 = 15V - 6V = 9V, and R1 = 3kΩ. We need to find R2.
Rearranging the equation to solve for R2: R2 = R1 * (V2 / V1)
Substituting the values:
R2 = 3kΩ * (9V / 6V)
R2 = 3kΩ * (3/2)
R2 = 4.5kΩ
Answer: 4.5kΩ
2.
Question 3
A variable potential divider is used in a simple voltage regulator circuit. Draw a circuit diagram of a variable potential divider used as a voltage regulator and explain how it functions.
Circuit Diagram:
| Vin |
| R1 |
| R2 (Variable Resistor) |
| Vout |
Functioning:
In a simple voltage regulator, a variable potential divider is used to create a stable output voltage from a potentially fluctuating input voltage. The input voltage (Vin) is applied across the series combination of R1 and the variable resistor R2. The output voltage (Vout) is taken from the junction between R1 and R2.
By carefully selecting the values of R1 and R2, and adjusting R2, a relatively constant output voltage can be maintained even if Vin varies. This is because the ratio of R1 and R2 ensures that the output voltage is a fraction of the input voltage. The variable resistor allows for fine adjustments to compensate for variations in Vin, providing a more stable Vout. This is a basic form of voltage regulation, although more sophisticated voltage regulators use other components like transistors.
3.
Two cells are connected in series and a constant current, I, is passed through them. A diagram of the circuit is shown below. The potential difference across each cell is given in the table. Calculate the value of the internal resistance of each cell. Explain your answer in terms of the relationship between potential difference, current, and resistance.
| Cell |
Potential Difference (V) |
Internal Resistance (Ω) |
| Cell 1 |
1.5 V |
Calculate |
| Cell 2 |
1.0 V |
Calculate |
To calculate the internal resistance, we can use the formula: r = V / I, where 'r' is the internal resistance, 'V' is the potential difference across the cell, and 'I' is the current.
For Cell 1: r1 = 1.5 V / I. Since the current is the same through both cells, we can substitute the value of 'I' from Cell 1's calculation into Cell 2's calculation.
For Cell 2: r2 = 1.0 V / I.
The internal resistance of Cell 1 is 1.5V / I. The internal resistance of Cell 2 is 1.0V / I. The internal resistance is directly proportional to the potential difference and inversely proportional to the current. Therefore, a lower potential difference across a cell indicates a higher internal resistance for a constant current. This is because a higher internal resistance means that more of the potential difference is 'lost' within the cell itself, leaving less potential difference available to overcome the external resistance in the circuit.