For the diode circuit which is shown in the figure, determine the current flowing through both the resistors and the diode. Assume that the diode is made of Silicon material.
Understand the Problem
The question is asking to determine the current flowing through the diodes and resistors in a given circuit setup with a 2V source and two resistors (4kΩ and 1kΩ) connected in series with the diode. To solve it, we will need to apply principles of circuit analysis, particularly Ohm's law and the characteristics of silicon diodes.
Answer
The current flowing through both the resistors and the diode is $I = 26mA$.
Answer for screen readers
The current flowing through both the resistors and the diode is $I = 26mA$.
Steps to Solve
- Identify the components and values in the circuit
The circuit consists of a voltage source of $2V$, and two resistors: $R_1 = 4k\Omega$ and $R_2 = 1k\Omega$, with a silicon diode connected in series with them.
- Calculate the total resistance in the circuit
Since the resistors are connected in series, the total resistance $R_{total}$ can be calculated as:
$$ R_{total} = R_1 + R_2 = 4k\Omega + 1k\Omega = 5k\Omega $$
- Determine the threshold voltage for the silicon diode
For a silicon diode, the typical forward voltage drop (threshold voltage) is approximately $0.7V$.
- Calculate the voltage across the resistors using the supply voltage and diode voltage drop
The voltage across the resistors is given by:
$$ V_R = V_{supply} - V_{diode} = 2V - 0.7V = 1.3V $$
- Apply Ohm's Law to find the current through the resistors and the diode
Using Ohm's Law ($I = \frac{V}{R}$), we can find the current $I$ flowing through the resistors:
$$ I = \frac{V_R}{R_{total}} = \frac{1.3V}{5k\Omega} = \frac{1.3}{5000} = 0.00026A = 26mA $$
The current flowing through both the resistors and the diode is $I = 26mA$.
More Information
This result shows the current through the diode, which is functioning in its conducting state since the voltage applied exceeds the forward voltage drop. The calculated current indicates that the components are operating within their limits.
Tips
- Ignoring Diode Voltage Drop: A common error is neglecting the diode's forward voltage drop. Always account for this when calculating the voltages in the circuit.
- Incorrect Resistance Addition: Ensure resistances connected in series are added correctly. Use $R_{total} = R_1 + R_2$.
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