To determine the current \(I_L\) in the circuit, follow these steps:
Identify the given values:
- Supply voltage (\(V_s\)) = 10 V
- Resistor \(R_1\) = 800 Ω
- Load resistor (\(R_L\)) = 1 kΩ = 1000 Ω
- Zener diode voltage (\(V_Z\)) = 5 V
Understand the Zener diode function:The Zener diode maintains a constant voltage (\(V_Z = 5\ V\)) across \(R_L\).
Calculate the current through the Zener diode: Since the Zener diode maintains a voltage of 5 V, the rest of the circuit can be assessed.
Calculate the voltage across \(R_1\):
\[V_{R1} = V_s - V_Z = 10\ V - 5\ V = 5\ V\]
Compute the current through \(R_1\) (Ohm's Law):
\[I_{R1} = \frac{V_{R1}}{R1} = \frac{5\ V}{800\ Ω} = 0.00625\ A = 6.25\ mA\]
Calculate the load current \(I_L\): For \(R_L\), use the voltage across it (5 V from the Zener diode):
\[I_L = \frac{V_Z}{R_L} = \frac{5\ V}{1000\ Ω} = 0.005\ A = 5\ mA\]
Validate the solution against the expected range: The computed \(I_L\) is 5 mA, which is within the specified range (5,5).
Thus, the current \(I_L\) through the load resistor when \(R_L = 1\ kΩ\) is 5 mA.
