DC Circuit | Numerical Solution

1. A cell of internal resistance of 0.2 Ω has connected two cells of resistance 6Ω and 8 Ω joined parallel. There is a current of 0.2 A in the 8 Ω coil. Find the emf of the cell. [Click here for Solution]

2076 B

Two resistors of resistance $1000 \; \Omega$ and $2000 \; \Omega$ are joined in series with a $100 \; V$ supply. A voltmeter of internal resistance $4000 \; \Omega$ is connected to measure the potential difference across $1000 \;  \Omega$ resistor. Calculate the reading shown by the voltmeter. [Click here for Solution]

2076 C / 2072 C

The resistance of a galvanometer coil is 9.36 Ω and the current required for full-scale deflection is 0.0224 A. We want to convert this galvanometer to an ammeter reading 20 A full scale. The only shunt available has a resistance of 0.025 Ω. What resistance must be connected in series with the coil? [Click here for Solution]

 

[2075 'A']

Two lamps rated 25 W - 220 V and 100 W - 220 V are connected to 220 V supply. Calculate the powers consumed by the lamps. [Click here for Solution]

[2075 'B']
Two resistance of 1000 Ω and 2000 Ω are placed in series with 50 V mains supply. What will be reading on a voltmeter of internal resistance 2000 Ω when placed across 1000 Ω resistor? What fractional change in voltmeter occurs when the voltmeter is connected? [Click here for Solution]

[2074 'B']
A copper wire has a diameter of 1.02 mm and carries a constant current of 1.67 A. If the density of free electrons in copper is $8.5\;*\;10^{28}/m^3$, calculate the current density and the drift velocity of the electrons. [Click here for Solution]

[2073 'Supp']
A battery of emf 1.5 V has a terminal p.d. of 1.25 V when a resistor of 25 Ω is joined to it. Calculate the current flowing, the internal resistance, and terminal p.d. when the resistance of 10 Ω replaces 25 Ω resistor. [Click here for Solution]

[2073 'C']
The resistance of a wire of length 1m, diameter 1 mm is 2.2 Ω. Calculate its resistivity and conductivity. [Click here for Solution]

[2073 'D']
An electric lamp consumes 60 W at 220 V. how many dry cells of emf 1.5 V and internal resistance 1 Ω are required to glow the lamp? [Click here for Solution]

[2072 'Supp']
A copper wire has a diameter of 1.02 mm, cross-sectional area $8.2 * 10^{-7}\; m^2$ and resistivity $1.72 * 10^{-8}\; \Omega \;m$. It carries 1.67 A. Find the electric field magnitude in the wire and the potential difference between two points in the wire 50 m apart. [Click here for Solution]

[2071 'Supp']

Consider the figure below. The current through 6 Ω resistor is 4 A in the direction shown.
What are the currents through the 25 Ω and 20 Ω resistors? [Click here for Solution]

[2071 'D']

In the given figure, the current through the 3 Ω resistor is 0.8 A. Find the potential drop across 4 Ω resistor. [Click here for Solution]

[2070 'Supp - A']
A cell of emf 18 V has an internal resistance of 3 Ω. The terminal p.d. of the battery becomes 15 V when connected by a wire. Find the resistance of the wire. [Click here for Solution]

[2070 'Supp - B']
A potential difference of 4.5 V is applied between the ends of the wire that are 2.5 m long and has a radius of 0.654 mm. The resulting current through the wire is 17.6 A. What is the resistivity of the wire? [Click here for Solution]

2070 C

A tightly coiled spring having 75 coils, each $3.5 \; cm$ in diameter, is made of insulated metal wire $3.25 \; mm$ in diameter. An ohmmeter connected across its opposite ends reads $1.74 \; \Omega$. What is the resistivity of the metal?

2070 D

A voltmeter coil has resistance $50 \; \Omega$ and a resistor of $1.15 \; K \Omega$ is connected in series. It can read potential differences up to $12 \; Volts$. If the same coil is used to construct an ammeter which can measure currents up to $2 \; A$, what should be the resistance of the shunt used?

2069 A

In the given figure, when switch $S$ is open, the voltmeter V reads $3.08 \; V$. When the switch is closed, the voltmeter reading drops to $2.97 \; V$ and the ammeter A reads $1.65 \; A$. Find the emf, the internal resistance of the battery, and the resistor R. Assume that the two meters are ideal.

2069 B

The resistance of a conductor is $10 \; \Omega$ at $50^{\circ}\; C$ and $15 \; \Omega$ at $100^{\circ}\; C$. Calculate its resistance at $0^{\circ}\; C$.

2068

An electric heating element to dissipate $1.2 \; kW$ on $240 \; V$ mains is to be made from nichrome ribbon $1\; mm$ wide and $0.05 \; mm$ thick. Calculate the length of the ribbon required if the resistivity of nichrome is $1.1 * 10^{-6} \; \Omega \;m$

2068 B

A resistor of $500 \; \Omega$ and one of $2000 \; \Omega$ are placed in series with a $60 \; Volt$ supply. What will be the reading on a voltmeter of internal resistance $2000 \; \Omega$ when placed across (i) the $500 \; \Omega$ resistor and (ii) the $2000 \; \Omega$ resistor?

2067 S

What is the potential difference across $100 \; \Omega$ resistor in the circuit given below?

2065

A galvanometer can bear a maximum current of $25 \; mA$ and resistance $5 \; \Omega$. Find the suitable resistance to convert it into (a) a voltmeter of range $0-2 \; V$ (b) an ammeter of range $0-10 \; Amp$.

2062

Twelve cells each of emf 2V and of internal resistance $0.5\; \Omega$ are arranged in a battery of n rows and an external resistance $0.4 \; \Omega$ is connected to the poles of the battery. Estimate the current flowing through the resistance in terms of n.

2061

As shown in the figure, a battery of emf $24 \;V$ and internal resistance $r$ is connected to a circuit containing two parallel resistors of $3\; Omega$ and $6\; \Omega$ in series with an $8\; \Omega$ resistor.

The current flowing in the $3\; \Omega$ is $0.8 \;A$. Calculate the current in the $6\; \Omega$ resistor and the internal resistance of the cell. 

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