A low resistance LDR of 20Ω, operated at a certain intensity of light, is to be protected through a series resistance in such a way that up to 12 mA of current is to flow at a supply voltage of 10 V. What is the nearest value of the protective resistance?

Concept:

Voltage division Rule:

\(\therefore {V_1} = \left( {\frac{{{R_1}}}{{{R_1} + {R_2}}}} \right) \times V\) 

\({V_2} = \left( {\frac{{{R_2}}}{{{R_1} + {R_2}}}} \right) \times V\) 

= Voltage across R₁ = Voltage across R₂

Calculation:

According to the question, we can draw circuit as:

By voltage division rule, we can write:

\({V_R} = \left( {\frac{R}{{R + 20}}} \right) \times 10\)     ---(1)

V_R = (12 × 10^-3) × R     ---(2)

From equation (1) and (2), we get:

\(\left( {12 \times {{10}^{ - 3}}} \right) \times R = \frac{{R \times 10}}{{R + 20}}\) 

\(12 + {10^{ - 3}} = \frac{{10}}{{R + 20}}\)

12 × 10^-3 R + 240 × 10^-3 = 10

12 × 10^-3 R = 9.76

\(R = \frac{{9.76}}{{12 \times {{10}^{ - 3}}}} = 813.33\;{\rm{\Omega }}\)

∴ R = 813 Ω

Hence, the nearest value of the protective resistance should be 813 Ω to protect LDR.

Important Points:

• LDR means light dependent resistor and it is also called a photoresistor.
• Light-dependent resistor values changes according to the intensity of light falling on it.
• LDR used as a light sensor to detect light.