In a metre bridge experiment, a standard resistor of 4.0\text{ }\Omega is connected in the… — JAMB UTME

In a metre bridge experiment, a standard resistor of $4.0\text{ }\Omega$ is connected in the left gap and an unknown resistor $R$ is connected in the right gap. When balanced, the balance point is found at a distance of $40.0\text{ cm}$ from the left end of the $100.0\text{ cm}$ bridge wire. What is the value of the unknown resistance $R$ in ohms?

Cevap: 6 Ω

Cevap

The value of the unknown resistance

R

6.0\text{ }\Omega

The metre bridge operates on the Wheatstone bridge principle. At balance, the ratio of the resistance in the left gap to the length of the left segment equals the ratio of the resistance in the right gap to the length of the right segment. Substituting

4.0\text{ }\Omega

for the left gap and

40.0\text{ cm}

and

60.0\text{ cm}

for the two wire lengths yields

R = 6.0\text{ }\Omega

Adım Adım Çözüm

Determine the length of the wire segment corresponding to the right gap.

l_2 = 100.0\text{ cm} - 40.0\text{ cm} = 60.0\text{ cm}

The total length of a standard metre bridge wire is

100.0\text{ cm}

Apply the Wheatstone bridge principle for the metre bridge balance condition.

\frac{R_{\text{left}}}{l_1} = \frac{R}{l_2} \implies R = R_{\text{left}} \times \frac{l_2}{l_1}

At balance, the potential drop per unit length across the two wire segments is proportional to their respective lengths.

Calculate the magnitude of the unknown resistor

R

R = 4.0 \times \frac{60.0}{40.0} = 6.0\text{ }\Omega

Multiplying and simplifying yields the exact resistance value.

Anahtar Kavram

Metre Bridge Principle (Wheatstone Bridge)

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru