1
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

Wheatstone bridge principle is used to measure the specific resistance $$\left(S_1\right)$$ of given wire, having length $$L$$, radius $$r$$. If $$X$$ is the resistance of wire, then specific resistance is ; $$S_1=X\left(\frac{\pi r^2}{L}\right)$$. If the length of the wire gets doubled then the value of specific resistance will be :

A
$$\frac{S_1}{4}$$
B
$$2 \mathrm{~S}_1$$
C
$$\frac{\mathrm{S}_1}{2}$$
D
$$S_1$$
2
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1

A wire of length $$10 \mathrm{~cm}$$ and radius $$\sqrt{7} \times 10^{-4} \mathrm{~m}$$ connected across the right gap of a meter bridge. When a resistance of $$4.5 \Omega$$ is connected on the left gap by using a resistance box, the balance length is found to be at $$60 \mathrm{~cm}$$ from the left end. If the resistivity of the wire is $$\mathrm{R} \times 10^{-7} \Omega \mathrm{m}$$, then value of $$\mathrm{R}$$ is :

A
63
B
70
C
66
D
35
3
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1

A wire of resistance $$\mathrm{R}$$ and length $$\mathrm{L}$$ is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

A
$$\frac{1}{25} \mathrm{R}$$
B
$$\frac{1}{5} R$$
C
25 R
D
5 R
4
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
For designing a voltmeter of range $50 \mathrm{~V}$ and an ammeter of range $10 \mathrm{~mA}$ using a galvanometer which has a coil of resistance $54 \Omega$ showing a full scale deflection for $1 \mathrm{~mA}$ as in figure.

(A) for voltmeter $R \approx 50 \mathrm{k} \Omega$

(B) for ammeter $\mathrm{r} \approx 0.2 \Omega$

(C) for ammeter $\mathrm{r}=6 \Omega$

(D) for voltmeter $R \approx 5 \mathrm{k} \Omega$

(E) for voltmeter $R \approx 500 \Omega$

Choose the correct answer from the options given below:
A
$(\mathrm{A})$ and $(\mathrm{C})$
B
(A) and (B)
C
(C) and (E)
D
(C) and (D)
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