Q: The V-I graph for a conductor at temperature \$T_{1}\$ and \$T_{2}\$ are as shown in the fig. The term \$(T_{2}-T_{1})\$ is proportional to

\$ V_{2} = tan(90-\theta)I_{2} V_{1} = tan\theta I_{1}\$\$ \Rightarrow V_{2} = cot\theta I_{2} \Rightarrow R_{1} = tan\theta\$\$ R_{2} = cot\theta\$\$ \Rightarrow (R_{2}-R_{1}) = R_{1} \alpha (T_{2}-T_{1})\$\$ \Rightarrow (T_{2}-T_{1}) \propto (R_{2}-R_{1})\$\$ \Rightarrow (T_{2}-T_{1}) \propto (\dfrac{cos^{2}\theta-sin^{2}\theta}{sin\theta cos\theta})\$\$ \Rightarrow (T_{2}-T_{1}) \propto \dfrac{cos2\theta}{sin2\theta}\$

Question 1

Express which of the following setups can be used to verify Ohms law?

Accepted Answer

In a circuit ammeter is always connected in series and voltmeter is always connected in parallel. So the option A is the correct setups for verifying Ohm's law.

Question 2

In the network shown, each resistance is equal to R. The equivalentresistance between diagonally opposite corners is:

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Question 3

Two non ideal batteries are connected in parallel. Consider the following statements:
1. The equivalent emf is smaller than either of the two emfs.
2. The equivalent internal resistance is smaller than either of the two internal resistances.

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Question 4

A coil of inductance 5H is joined to a cell of emf 6V through a resistance $10\Omega $ time t = 0. The emf  across the coil at time t =$ln\sqrt{2}s is ;$

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Question 5

In the given circuit, no cur rent is passing through the galvanometer. If the cross-sectional diameter of AB is doubled then for null point of galvanometer the value of AC would

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Question 6

In the figure, the potentiometer wire AB of length L and resistance $9 r$ is joined to the cell D of emf $ε$ and internal resistance r. The cell Cs emf is $ϵ / 2$ and its internal resistance is $2 r$ . The galvanometer G will show no deflection when the length AJ is

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Question 7

When a magnet is being moved towards a coil, the induced emf does not depend upon:

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Question 8

The V-I graph for a conductor at temperature $T_{1}$ and $T_{2}$ are as shown in the fig. The term $(T_{2}-T_{1})$ is proportional to

Accepted Answer

$ V_{2} = tan(90-\theta)I_{2}              V_{1} = tan\theta I_{1}$$ \Rightarrow  V_{2} = cot\theta I_{2}         \Rightarrow R_{1} = tan\theta$$ R_{2} = cot\theta$$ \Rightarrow (R_{2}-R_{1}) = R_{1} \alpha (T_{2}-T_{1})$$ \Rightarrow  (T_{2}-T_{1}) \propto (R_{2}-R_{1})$$ \Rightarrow  (T_{2}-T_{1}) \propto (\dfrac{cos^{2}\theta-sin^{2}\theta}{sin\theta cos\theta})$$ \Rightarrow  (T_{2}-T_{1}) \propto  \dfrac{cos2\theta}{sin2\theta}$

Question 9

The potentiometer wire AB is made of two equal parts AN and NB of cross sectional radius $2 r$ and $r$ respectively.The material of both parts is same. A cell is connected between A and B. The potential gradient in the part AN is $1 V / m$ . Potential difference between two points C and D(shown in figure) separated by $20 c m$ is found to be $0.5 V$ . The separation between C and N is $\frac{t}{3}$ cm. Then $t$ is

Accepted Answer

The potentiometer wire AB is made of two parts AN and NB of cross sectional radii 2r and r respectively. Hence, the cross sectional area of the parts AN and NB are in the ratio 1 :4 and the resistance per unit length will be in the ratio 4:1.Therefore the potential gradient in the part NB will be four times that in the part AN.i.e. $V_{NB} = 4 V_{AN}$But, $V_{AN} = 1 V$$V_{NB} = 4 V$Let, $CN = x m$ From above discussion,$ND = (0.2-x) m$Now, $V_{CD} = V_{CN}x + (0.2-x)\times 4$$0.5 = (1)x + (0.8-4x)$$(0.3)x = 0.3$$\therefore x = 0.1m$ But, $CN = \dfrac {t}{3}$ i.e. $x = \dfrac {t}{3}$Hence, $ 0.1m = (\dfrac {t}{3})cm$$\therefore t = 0.3 m = 30cm$

Question 10

Find the value of series of combination of resistance R and X in $\Omega $

Accepted Answer

For potentiometer the voltage source is providing constant current in the circuit and if $R$ and $X$ are connected in series it will form Wheatstone's network so the balancing condition is$\dfrac {X}{R}= \dfrac{70}{60}$$ X = \dfrac {7\times 12}{6} = 14\Omega$equivalent resistance of $R$ and $X$ in series$=R+X= 26 \;ohms$.Hence, correct answer is option B.

Current Electricity

Physics
11903 Views

Express which of the following setups can be used to verify Ohms law?

In the network shown, each resistance is equal to R. The equivalent
resistance between diagonally opposite corners is:

Two non ideal batteries are connected in parallel. Consider the following statements:
1. The equivalent emf is smaller than either of the two emfs.
2. The equivalent internal resistance is smaller than either of the two internal resistances.

A coil of inductance 5H is joined to a cell of emf 6V through a resistance $10 Ω$ time t = 0. The emf across the coil at time t = $l n 2 s i s;$

In the given circuit, no cur rent is passing through the galvanometer. If the cross-sectional diameter of AB is doubled then for null point of galvanometer the value of AC would

In the figure, the potentiometer wire AB of length L and resistance $9 r$ is joined to the cell D of emf $ε$ and internal resistance r. The cell Cs emf is $ϵ / 2$ and its internal resistance is $2 r$ . The galvanometer G will show no deflection when the length AJ is

When a magnet is being moved towards a coil, the induced emf does not depend upon:

The V-I graph for a conductor at temperature $T_{1}$ and $T_{2}$ are as shown in the fig. The term $(T_{2} - T_{1})$ is proportional to

Find the value of series of combination of resistance R and X in $Ω$

Current Electricity

Physics 11903 Views

Express which of the following setups can be used to verify Ohms law?

In the network shown, each resistance is equal to R. The equivalent resistance between diagonally opposite corners is:

Two non ideal batteries are connected in parallel. Consider the following statements: 1. The equivalent emf is smaller than either of the two emfs. 2. The equivalent internal resistance is smaller than either of the two internal resistances.

A coil of inductance 5H is joined to a cell of emf 6V through a resistance 10Ω time t = 0. The emf across the coil at time t =ln2​sis;

In the given circuit, no cur rent is passing through the galvanometer. If the cross-sectional diameter of AB is doubled then for null point of galvanometer the value of AC would

In the figure, the potentiometer wire AB of length L and resistance 9r is joined to the cell D of emf ε and internal resistance r. The cell Cs emf is ϵ/2 and its internal resistance is 2r. The galvanometer G will show no deflection when the length AJ is

When a magnet is being moved towards a coil, the induced emf does not depend upon:

The V-I graph for a conductor at temperature T1​ and T2​ are as shown in the fig. The term (T2​−T1​) is proportional to

Find the value of series of combination of resistance R and X in Ω

Physics
11903 Views

In the network shown, each resistance is equal to R. The equivalent
resistance between diagonally opposite corners is:

Two non ideal batteries are connected in parallel. Consider the following statements:
1. The equivalent emf is smaller than either of the two emfs.
2. The equivalent internal resistance is smaller than either of the two internal resistances.

A coil of inductance 5H is joined to a cell of emf 6V through a resistance $10 Ω$ time t = 0. The emf across the coil at time t = $l n 2 s i s;$

In the figure, the potentiometer wire AB of length L and resistance $9 r$ is joined to the cell D of emf $ε$ and internal resistance r. The cell Cs emf is $ϵ / 2$ and its internal resistance is $2 r$ . The galvanometer G will show no deflection when the length AJ is

The V-I graph for a conductor at temperature $T_{1}$ and $T_{2}$ are as shown in the fig. The term $(T_{2} - T_{1})$ is proportional to

Find the value of series of combination of resistance R and X in $Ω$