###### Advertisements

###### Advertisements

A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

###### Advertisements

#### Solution

Emf of the battery, E = 10 V

The internal resistance of the battery, r = 3 Ω

Current in the circuit, I = 0.5 A

Resistance of the resistor = R

The relation for current using Ohm’s law is,

I = `"E"/("R" + "r")`

R + r = `"E"/"I"`

= `10/0.5`

= 20 Ω

∴ R = 20 − 3 = 17 Ω

Terminal voltage of the resistor = V

According to Ohm’s law,

V = IR

= 0.5 × 17

= 8.5 V

Therefore, the resistance of the resistor is 17 Ω, and the terminal voltage is 8.5 V.

#### APPEARS IN

#### RELATED QUESTIONS

Two cells of emfs 1.5 V and 2.0 V, having internal resistances 0.2 Ω and 0.3 Ω, respectively, are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.

In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm, what is the emf of the second cell?

A secondary cell after long use has an emf of 1.9 V and a large internal resistance of 380 Ω. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

A long straight current carrying wire passes normally through the centre of circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify.

The equivalent resistance between points. a and f of the network shown in Figure 2 is :

a) 24 Ω

b) 110 Ω

c) 140 Ω

d) 200 Ω

A resistor R is connected to a cell of-emf e and internal resistance r. The potential difference across the resistor R is found to be V. State the relation between e, V, Rand r.

A cell of emf ‘E’ and internal resistance ‘r’ draws a current ‘I’. Write the relation between terminal voltage ‘V’ in terms of E, I and r ?

Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with each other across an external resistance R. What is the current through this resistance?

A cell of emf ‘*E*’ and internal resistance ‘*r*’ is connected across a variable resistor ‘*R*’. Plot a graph showing the variation of terminal potential ‘*V*’ with resistance R. Predict from the graph the condition under which ‘*V*’ becomes equal to ‘*E*’.

Can the potential difference across a battery be greater than its emf?

Two non-ideal batteries are connected in series. Consider the following statements:-

(A) The equivalent emf is larger than either of the two emfs.

(B) The equivalent internal resistance is smaller than either of the two internal resistances.

Find the value of i_{1}/i_{2} in the following figure if (a) R = 0.1 Ω (b) R = 1 Ω and (c) R = 10 Ω. Note from your answers that in order to get more current from a combination of two batteries, they should be joined in parallel if the external resistance is small and in series if the external resistance is large, compared to the internal resistance.

Consider N = n_{1}n_{2}_{ }identical cells, each of emf ε and internal resistance r. Suppose n_{1} cells are joined in series to form a line and n_{2} such lines are connected in parallel.

The combination drives a current in an external resistance R. (a) Find the current in the external resistance. (b) Assuming that n_{1} and n_{2} can be continuously varied, find the relation between n_{1}, n_{2}, R and r for which the current in R is maximum.

Do all thermocouples have a neutral temperature?

Do the electrodes in an electrolytic cell have fixed polarity like a battery?

A coil of resistance 100 Ω is connected across a battery of emf 6.0 V. Assume that the heat developed in the coil is used to raise its temperature. If the heat capacity of the coil is 4.0 J K^{−1}, how long will it take to raise the temperature of the coil by 15°C?

The temperatures of the junctions of a bismuth-silver thermocouple are maintained at 0°C and 0.001°C. Find the thermo-emf (Seebeck emf) developed. For bismuth-silver, a = − 46 × 10^{−6} V°C^{−1} and b = −0.48 × 10^{−6} V°C^{−2}.

Find the emf of the battery shown in the figure:

**Answer the following question.**

What is the end error in a meter bridge? How is it overcome? The resistances in the two arms of the metre bridge are R = Ω and S respectively. When the resistance S is shunted with equal resistance, the new balance length found to be 1.5 l_{1}, where l_{2} is the initial balancing length. calculate the value of s.

A conductor of length 'l' is rotated about one of its ends at a constant angular speed 'ω' in a plane perpendicular to a uniform magnetic field B. Plot graphs to show variations of the emf induced across the ends of the conductor with (i) angular speed ω and (ii) length of the conductor l.

Two cells of emfs approximately 5 V and 10 V are to be accurately compared using a potentiometer of length 400 cm.

A cell having an emf E and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by ______.

Five cells each of emf E and internal resistance r send the same amount of current through an external resistance R whether the cells are connected in parallel or in series. Then the ratio `("R"/"r")` is:

The internal resistance of a cell is the resistance of ______

A cell E_{1} of emf 6 V and internal resistance 2 Ω is connected with another cell E_{2} of emf 4 V and internal resistance 8 Ω (as shown in the figure). The potential difference across points X and Y is ______.

A battery of EMF 10V sets up a current of 1A when connected across a resistor of 8Ω. If the resistor is shunted by another 8Ω resistor, what would be the current in the circuit? (in A)

A block of metal is heated directly by dissipating power in the internal resistance of block. Because of temperature rise, the resistance increases exponentially with time and is given by R(t) = 0.5 e^{2t}, where t is in second. The block is connected across a 110 V source and dissipates 7644 J heat energy over a certain period of time. This period of time is ______ × 10^{-1} sec (take ln 0.367 = -1).

An ac generator generates an emf which is given by e = 311 sin (240 πt) V. Calculate:

- frequency of the emf.
- r.m.s. value of the emf.