A candidate connects a moving coil voltmeter \(V\), a moving coil ammeter \(A\), and a resistor \(R\) as shown in Fig. 6.58. If the voltmeter reads \(20~\text{V}\) and the ammeter reads \(4~\text{A}\), \(R\) is: 

1. equal to \(5~\Omega\)
2.  greater than \(5~\Omega\)
3.  less than \(5~\Omega\)
4. greater or less than \(5~\Omega\) depending upon its material.

A galvanometer has a resistance of 3663 $\Omega$. A shunt S is connected across it such that 1/34 of the total current passes through the galvanometer. The value of the shunt is :

(1) 3663 $\Omega$

(2) 111 $\Omega$

(3) 107.7 $\Omega$

(4) 3555.3 $\Omega$

Two toroids \(1\) and \(2\) have total no. of turns \(200\) and \(100\) respectively with average radii \(40~\text{cm}\) and \(20~\text{cm}\) respectively. If they carry the same current \(i,\) what will be the ratio of the magnetic fields along the two loops?
1. \(1:1\)
2. \(4:1\)
3. \(2:1\)
4. \(1:2\)

A straight conductor carrying current \(I\) splits into two parts as shown in the figure. The radius of the circular loop is \(R\). The total magnetic field at the centre \(P\) of the loop is:

A milliammeter of range 10 mA and resistance 9$\Omega$ is joined in a circuit as shown in Fig. 6.57. The meter gives full-scale deflection for current I when A and C are used as its terminals if current enter at A and leaves at C (B is left isolated). The value of I is :

(1)100 mA

(2) 900 mA

(3) 1 A

(4) 1.1 A

The endpoints of a current-carrying wire lie on the x-axis and y-axis as shown. The magnetic force on the wire is:

1. Zero

2. 6 N

3. 8 N

4. 10 N

The given figure shows a semicircular loop of radius R carrying current I and is placed in a uniform magnetic field B. The force acting on the semicircular part of the loop is

1. $B_0\pi lR$

2. $2\mathrm{\pi lRB}$

3. $lRB$

4. $2lRB$

A non-conducting rod AB of length L has a positive linear charge density $\lambda$. This rod is rotated about its one end with an angular speed $\omega$ as shown. The magnetic moment associated with this rod is-

1. λ$\frac{L^3\omega }{3}$

2. λ$\frac{L^3\omega }{6}$

3. $\frac{\pi L^3\omega }{12}$

4. $\frac{\pi L^3\omega }{24}$