Physics Multiple Choice Questions on “Current Electricity – Meter Bridge”.

1. Two resistances are connected in two gaps of Meter Bridge. The balance is 20cm from the zero end. A resistance of 15 ohms is connected in series with the smaller of the two. The null point shifts to 40cm. What is the value of the bigger resistance?

a) 9

b) 18

c) 27

d) 36

Answer: d

Clarification: Let P be the smaller resistance and Q be the bigger resistance.

First case → (frac {P}{Q} = frac {20}{80} = frac {1}{4})

Second case → (frac {(P+15)}{Q} = frac {40}{60} = frac {2}{3})

Comparing both → (frac {P}{(P + 15)} = frac {1}{4} , times , frac {3}{2} = frac {3}{8})

8P = 3P + 45 → 5P = 45 → P = 9 ohms

Therefore, substituting in (frac {P}{Q} = frac {1}{4}) → (frac {9}{Q} = frac {1}{4}) → Q = 36 ohms.

2. What is the effect on null deflection of galvanometer, when the radius of the wire is tripled?

a) No change

b) Becomes half

c) Reduces by (frac {1}{3})

d) Thrice the original value

Answer: a

Clarification: For a balanced Meter Bridge (frac {P}{Q} = frac {x}{(100-x)}). From this, we can understand that the null deflection of galvanometer does not depend on the radius of the wire. So, even if the radius of the wire is tripled, the null deflection of the galvanometer undergoes no change.

3. A resistance of 5 ohms is connected across the gap of a Meter Bridge and an unknown resistance, greater than 5 ohms, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 50 cm. Neglecting any correction, what is the unknown resistance? The length of the wire is 150 cm.

a) 3 ohms

b) 10 ohms

c) 7 ohms

d) 5 ohms

Answer: b

Clarification: Let × be the unknown resistance.

First case → (frac {5}{x} = frac {l}{(150 – l)})

750 – 5l = xl ……….. 1

Second case → (frac {x}{5} = frac {(l + 50)}{(100 – l)})

100 – xl = 5l + 250

xl = 100x – 5l – 250 ………… 2

Comparing 1 and 2

750 – 5l = 100x – 5l – 250

100x = 750 + 250

100x = 1000

x = 10 ohms

Therefore, the unknown resistance is 10 ohms.

4. The sensitivity of the meter bridge is at the peak when all resistors have the same order.

a) True

b) False

Answer: a

Clarification: Yes, the sensitivity of the meter bridge is at the peak when all resistors have the same order. The sensitivity can be increased by keeping the current in the galvanometer high and this can be achieved by reducing the values of the resistors used in the Meter Bridge.

5. Which error is removed when the known and unknown resistances are interchanged in a Meter Bridge?

a) Percentage error

b) Measurement error

c) End error

d) Index error

Answer: c

Clarification: End error is removed when the known and unknown resistances are interchanged in a Meter Bridge. This additional length has a resistance known as end resistance. So, when an end error arises, it can be removed by interchanging the known and unknown resistances and taking the mean of the resistances determined.