An a.c. voltage of peak value 20 V is connected in series with a silicon diode and load resistance of 500 Ω. If the forward resistance of diode is 10 Ω, find :

1. Break Down the Problem

We need to analyze the circuit involving an alternating current (AC) voltage, a silicon diode, and a load resistance. The parameters given are:

• Peak voltage ($V_m$): 20 V
• Load resistance ($R_L$): 500 Ω
• Diode forward resistance ($R_d$): 10 Ω

We are to find the effective voltage across the load resistance when connected in the circuit.

2. Relevant Concepts

To find the voltage across the load resistance in a circuit with a diode, we will do the following:

• Calculate the total resistance ($R_{total}$) in the circuit.
• Determine the current ($I$) flowing through the circuit using Ohm's Law.
• Calculate the voltage across the load resistance ($V_{L}$).

3. Analysis and Detail

1. Calculate Total Resistance: $R_{total} = R_L + R_d = 500 \, \Omega + 10 \, \Omega = 510 \, \Omega$

2. Calculate the RMS Voltage: The peak voltage needs to be converted to the root mean square (RMS) voltage. The RMS value for an AC voltage is given by: $V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{20}{\sqrt{2}} \approx 14.14 \, V$

3. Calculate Current Using Ohm's Law: The total current in the circuit can be calculated as: $I = \frac{V_{rms}}{R_{total}} = \frac{14.14}{510} \approx 0.0277 \, A$

4. Calculate Voltage Across Load Resistance: The voltage across the load resistance ($V_L$) can be calculated as: $V_L = I \times R_L = 0.0277 \times 500 \approx 13.85 \, V$

4. Verify and Summarize

• Total resistance was calculated correctly.
• The RMS voltage was determined with the correct formula.
• The current was calculated using Ohm's Law with the derived resistances, and the voltage across the load was correctly computed.

Final Answer

The voltage across the load resistance is approximately 13.85 V.