Advertisements
Advertisements
Question
A cell of e.m.f 1.5V and negligible internal resistance is connected in series with a potential meter of length 10 m and the total resistance of 20 Ω. What resistance should be introduced in the resistance box such that the potential drop across the potentiometer is one microvolt per cm of the wire?
Advertisements
Solution
Given:
R = 20 Ω, L = 10 m, E = 1.5 V,
K = 1 μV/cm = 1 × (10-6 /10-2 ) V/ m
= 10-4 V/ m
To find: External resistance (RE)
Formula: K = `"V"/"L"`
Calculation:
Since, I = `"E"/("R" + "R"_"E")`
Also, V = IR = `"ER"/("R" + "R"_"E")`
From formula,
K = `"ER"/(("R" + "R"_"E")"L")`
R + RE = `"ER"/"KL"`
∴ RE = `(1.5 xx 20)/(10^-4 xx 10) - 20 = 30000 - 20`
∴ RE = 29980 Ω
The external resistance should be 29980 Ω.
APPEARS IN
RELATED QUESTIONS
On what factors does the potential gradient of the wire depend?
Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Ω maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents up to a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, very high resistance of 600 kΩ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf ε and the balance point found similarly, turns out to be at 82.3 cm length of the wire.
(a) What is the value ε?
(b) What purpose does the high resistance of 600 kΩ have?
(c) Is the balance point affected by this high resistance?
(d) Is the balance point affected by the internal resistance of the driver cell?
(e) Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0 V instead of 2.0 V?
(f) Would the circuit work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of a thermo-couple)? If not, how will you modify the circuit?
In the given circuit, with steady current, calculate the potential drop across the capacitor and the charge stored in it.
In the given circuit in the steady state, obtain the expressions for (a) the potential drop (b) the charge and (c) the energy stored in the capacitor, C.
State the principle of a potentiometer. Define potential gradient. Obtain an expression for potential gradient in terms of resistivity of the potentiometer wire.
Figure shows a long potentiometer wire AB having a constant potential gradient. The null points for the two primary cells of emfs ε1 and ε2 connected in the manner shown are obtained at a distance of l1 = 120 cm and l2 = 300 cm from the end A. Determine (i) ε1/ε2 and (ii) position of null point for the cell ε1 only.
State the working principle of a potentiometer. With the help of the circuit diagram, explain how a potentiometer is used to compare the emf's of two primary cells. Obtain the required expression used for comparing the emfs.
In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emfs ε1 and ε2 connected in the manner shown are obtained at a distance of 120 cm and 300 cm from the end A. Find (i) ε1/ ε2 and (ii) position of null point for the cell ε1.
How is the sensitivity of a potentiometer increased?
Write the principle of working of a potentiometer. Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell.
The potentiometer wire AB shown in the figure is 40 cm long. Where should the free end of the galvanometer be connected on AB, so that the galvanometer may show zero deflection?
In a potentiometer experiment, the balancing length with a resistance of 2Ω is found to be 100 cm, while that of an unknown resistance is 500 cm. Calculate the value of the unknown resistance.
Define potential gradient of the potentiometer wire.
Why should not the jockey be slided along the potentiometer wire?
How is potential gradient measured? Explain.
Distinguish between a potentiometer and a voltmeter.
Describe how a potentiometer is used to compare the EMFs of two cells by connecting the cells individually.
Describe with the help of a neat circuit diagram how you will determine the internal resistance of a cell by using a potentiometer. Derive the necessary formula.
A potentiometer wire has a length of 1.5 m and a resistance of 10 Ω. It is connected in series with the cell of emf 4 Volt and internal resistance 5 Ω. Calculate the potential drop per centimeter of the wire.
When two cells of emf's E1 and E2 are connected in series so as to assist each other, their balancing length on a potentiometer wire is found to be 2.7 m. When the cells are connected in series so as to oppose each other, the balancing length is found to be 0.3 m. Compare the emf's of the two cells.
The SI unit of the potential gradient is ______
If the potential gradient of a wire decreases, then its length ______
The instrument which can measure terminal potential difference as well as electromotive force (emf) is ______
To determine the internal resistance of a cell by using potentiometer, the null point is at 1 m when cell is shunted by 3 Ω resistance and at a length 1.5 m when cell is shunted by 6 Ω resistance. The internal resistance of the cell is ______.
In the experiment to determine the internal resistance of a cell (E1) using a potentiometer, the resistance drawn from the resistance box is 'R'. The potential difference across the balancing length of the wire is equal to the terminal potential difference (V) of the cell. The value of internal resistance (r) of the cell is ______
A potentiometer wire has a length of 4m and resistance of 5Ω. It is connected in series with 495 Ω resistance and a cell of e.m.f. 4V. The potential gradient along the wire is ______
Two students X and Y perform potentiometer experiment separately and null point was obtained as shown in diagram. During the experiment, ______.
- X increases the value of R (resistance)
- Y decreases the value of S (resistance)
The position of null point obtained by students X and Y respectively.
In a potentiometer experiment when three cells A, B, C are connected in series the balancing length is found to be 740 cm. If A and B are connected in series, the balancing length is 440 cm and when B and C are connected in series, it is 540 cm. The e.m.f. of A, B, and C cells EA, EB, EC are respectively (in volt) ______
In a potentiometer experiment, for measuring internal resistance of a cell, the balance point has been obtained on the fourth wire. The balance point can be shifted to fifth wire by ______.
A battery is connected with a potentiometer wire. The internal resistance of the battery is negligible. If the length of the potentiometer wire of the same material and radius is doubled then ______.
A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves ______.
In a potentiometer of 10 wires, the balance point is obtained on the 7th wire. To shift the balance point to 9th wire, we should ______.
AB is a wire of potentiometer with the increase in the value of resistance R, the shift in the balance point J will be ______.
AB is a wire of potentiometer with the increase in value of resistance R, the shift in the balance point J will be:
Specific resistance of a conductor increase with.
1°C rise in temperature is observed in a conductor by passing a certain current. If the current is double then the rise in temperature is approximately.
In an experiment with a potentiometer, VB = 10V. R is adjusted to be 50Ω (Figure). A student wanting to measure voltage E1 of a battery (approx. 8V) finds no null point possible. He then diminishes R to 10Ω and is able to locate the null point on the last (4th) segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.
For the circuit shown, with R1 = 1.0 Ω, R2 = 2.0 Ω, E1 = 2 V, and E2 = E3 = 4 V, the potential difference between the points 'a' and 'b' is approximately (in V) ______.
As a cell age, its internal resistance increases. A voltmeter of resistance 270 Ω connected across an old dry cell reads 1.44 V. However, a potentiometer at the balance point gives a voltage measurement of the cell as 1.5 V. Internal resistance of the cell is ______ Ω.
Two identical thin metal plates has charge q1 and q2 respectively such that q1 > q2. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is ______.
Two cells of same emf but different internal resistances r1 and r2 are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is ______.
A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r. A cell C having emt `ε/2` and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in the figure shows no deflection is ______.
What is the value of resistance for an ideal voltmeter?
A particle carrying 8 electron charges starts from rest and is accelerated through a potential difference of 9000 V. Calculate the KE acquired by it in keV.
Draw a neat labelled diagram of Internal resistance of a cell using a potentiometer.
State dimension of potential gradient.
Draw neat labelled diagram of potentiometer as voltage divider.
Three identical cells each of emf 'e' are connected in parallel to form a battery. What is the emf of the battery?
