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Find the equivalent resistance between two opposite corners of a square formed by a wire of resistance 20 Ω.
5 Ω
Calculate the total resistance in a circuit where two resistors of 10 Ω and 20 Ω are connected in parallel and then in series with a 5 Ω resistor.
9.0 Ω
What is the current flowing through a 5 Ω resistor connected to a 10 V battery?
2 A
Find the potential gradient of a potentiometer wire of length 1 m and resistance 4 Ω with a 2 V cell connected across it.
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What will be the new resistance of a wire that has a resistance of 9 Ω and is stretched to double its length?
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Calculate the current passing through a 2 Ω resistor if a potential difference of 12 V is applied.
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Find the power dissipated in a 4 Ω resistor when a current of 3 A flows through it.
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What is the current in a circuit with a cell of EMF 5 V and internal resistance 0.5 Ω connected to an external resistance of 9.5 Ω?
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What should be the resistance of the unknown resistor in a Wheatstone bridge with the ratio arms of 3 Ω and 5 Ω, when the fourth resistor is 10 Ω?
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Find the current if two resistors of resistance 2 Ω and 3 Ω are connected in series with a 10 V battery.
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Find the shunt resistance required to convert a galvanometer with resistance 50 Ω into an ammeter of range 1 A when the current required for full-scale deflection is 2 mA.
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Calculate the heat produced in 10 seconds by a heater coil with a resistance of 30 Ω connected to a 120 V power supply.
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Calculate the drift velocity of electrons in a copper wire of cross-sectional area $10^{-6} m^2$ when a current of 5 A flows through it.
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Find the time constant of a circuit with a capacitor of 5 µF charged by a 12 V battery and connected to a resistor of 2 MΩ.
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Calculate the temperature coefficient of resistance if the resistance of a conductor increases by 20% when its temperature is raised from 27°C to 127°C.
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A current of 2 A flows through a conductor when a potential difference of 6 V is applied. What is the resistance of the conductor?
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If the current through a conductor doubles, how does the power dissipated in the conductor change?
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Two resistors, 4 Ω and 6 Ω, are connected in series and a voltage of 20 V is applied. What is the power dissipated in the 6 Ω resistor?
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A 60 W bulb is connected to a 120 V supply. What is the resistance of the bulb?
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Which of the following is true for a parallel circuit?
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A wire has a resistance of 8 Ω. If its length is doubled, what will be its new resistance?
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The internal resistance of a cell decreases with:
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A copper wire of length 2 m and cross-sectional area 1 mm² has a resistance of 0.34 Ω. What will be the resistance of a wire of the same material with length 4 m and cross-sectional area 2 mm²?
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In a series circuit, which of the following remains constant across all components?
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The resistivity of a material depends on:
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In an electric circuit, the potential difference across the ends of a resistor is 10 V and the current passing through it is 5 A. What is the resistance?
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The power dissipated in a resistor of resistance 10 Ω when a current of 3 A flows through it is:
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Which law states that the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature remains constant?
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The SI unit of electric resistivity is:
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The energy dissipated in the form of heat in a resistor when a current 'I' flows through it for a time 't' is given by:
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Study Notes
Current Electricity
- Resistance of a Square: When a wire of resistance 20 Ω is bent to form a square, the equivalent resistance between opposite corners is 5 Ω. This is because the wire is divided into four equal resistors, and the resistance of two resistors in parallel is half the resistance of one resistor.
- Parallel and Series Resistors: When a 10 Ω resistor and a 20 Ω resistor are connected in parallel, the total resistance is 6.67 Ω. Then, when connected in series with a 5 Ω resistor, the total resistance becomes 11.67 Ω.
- Ohm's Law: The current flowing through a 5 Ω resistor when connected to a 10 V battery is 2 A. This is calculated using Ohm's Law: I = V/R, where I is current, V is voltage, and R is resistance.
- Potential Gradient: The potential gradient of a 1 m long wire with a resistance of 4 Ω, connected to a 2 V cell, is 2 V/m. This is calculated by dividing the voltage by the length of the wire.
- Resistance and Length: When a wire with a resistance of 9 Ω is stretched to double its length, its resistance increases to 36 Ω. This is attributed to the fact that resistance is directly proportional to the length of the wire.
- Power Dissipation: The power dissipated in a 4 Ω resistor with a 3 A current flowing through it is 36 W. Power is calculated using the formula P = I²R, where P is power, I is current, and R is resistance.
- Internal Resistance: A cell with an EMF of 5 V and internal resistance of 0.5 Ω, connected to an external resistance of 9.5 Ω, will have a current flow of 0.5 A. This is calculated using the formula I = EMF / (R + r), where EMF is electromotive force, R is external resistance, and r is internal resistance.
- Wheatstone Bridge: In a balanced Wheatstone bridge, the resistance of the unknown resistor can be calculated with the formula R_unknown = (R_2 * R_4) / R_1, where R_1, R_2 are the resistances in the ratio arms, and R_4 is the known resistor. If R_1 = 3 Ω, R_2 = 5 Ω, and R_4 = 10 Ω, the unknown resistance is 16.67 Ω.
- Series Resistors: Two resistors with resistances 2 Ω and 3 Ω connected in series will have a total resistance of 5 Ω. When connected to a 10 V battery, the current through the circuit will be 2 A.
- Shunt Resistance: To convert a galvanometer with a full-scale deflection current of 2 mA and a resistance of 50 Ω into an ammeter with a range of 1 A, a shunt resistance of 0.1 Ω is required.
- Heat Production: A heater coil with a resistance of 30 Ω connected to a 120 V power supply will produce 480 J of heat in 10 seconds. The heat produced is calculated using the formula H = I²Rt, where H is heat, I is current, R is resistance, and t is time.
- Drift Velocity: The drift velocity of electrons in a copper wire with a cross-sectional area of 10^-6 m^2, carrying a 5 A current, is 3.68 x 10^-5 m/s. The drift velocity can be calculated using the formula v_d = I / (nAe), where v_d is drift velocity, I is current, A is cross-sectional area, n is electron density, and e is the charge of an electron.
- Time Constant: The time constant of an RC circuit with a 5 µF capacitor charged by a 12 V battery and then connected to a 2 MΩ resistor is 10 seconds. The time constant is calculated by multiplying the capacitance and resistance.
- Temperature Coefficient of Resistance: If the resistance of a conductor increases by 20% when its temperature is raised from 27°C to 127°C, the temperature coefficient of resistance of the material is 0.002/°C. The temperature coefficient is calculated using the formula α = (R_2 - R_1) / (R_1 * (T_2 - T_1)), where α is the temperature coefficient, R_1 is the resistance at temperature T_1, and R_2 is the resistance at temperature T_2.
Multiple Choice Questions
- Resistance Calculation: The resistance of a conductor with a current of 2 A flowing through it when a potential difference of 6 V is applied is 3 Ω. This is calculated using Ohm's Law (R = V/I).
- Power and Current: If the current through a conductor doubles, the power dissipated in the conductor quadruples. Power is proportional to the square of the current (P = I²R).
- Power Dissipation in Series Circuit: The power dissipated in the 6 Ω resistor in a series circuit with a 4 Ω resistor and a 20 V voltage applied is 8 W. This is calculated using the formula for power in a resistor (P = V²/R) after first determining the current flowing through the circuit.
- Resistance of a Bulb: The resistance of a 60 W bulb connected to a 120 V supply is 240 Ω. This is calculated using the formula P = V²/R and solving for resistance.
- Parallel Circuit Characteristics: In a parallel circuit, the voltage is the same across all resistors. This is a key characteristic of parallel circuits.
- Resistance and Length: If you double the length of a wire with a resistance of 8 Ω, you double its resistance. Resistance is directly proportional to the length of the wire.
- Internal Resistance and Temperature: The internal resistance of a cell decreases with increasing temperature. Increasing temperature reduces the resistivity of the electrolyte, leading to a decrease in internal resistance.
- Resistance and Dimensions: The resistance of a copper wire with a length of 4 m and a cross-sectional area of 2 mm² is 0.68 Ω. Resistance is proportional to length and inversely proportional to cross-sectional area.
- Series Circuit Constant: In a series circuit, the current remains constant across all components. This is because the same current flows through each component in a series circuit.
- Resistivity Dependence: The resistivity of a material depends on the material and temperature. Resistivity is an inherent property of a material and is influenced by temperature changes.
- Resistance Calculation: If the potential difference across the ends of a resistor is 10 V and the current passing through it is 5 A, the resistance is 2 Ω. This is calculated using Ohm's Law (R = V/I).
- Power Dissipation in a Resistor: The power dissipated in a 10 Ω resistor when a current of 3 A flows through it is 90 W. This is calculated using the formula P = I²R.
- Ohm's Law: The law that states the current flowing through a conductor is directly proportional to the potential difference across its ends, assuming constant temperature, is called Ohm's Law.
- Resistivity Unit: The SI unit of electric resistivity is Ohm-meter (Ω⋅m). Resistivity is a measure of the resistance of a material to electrical current flow.
- Electrical Energy Dissipation: The energy dissipated in the form of heat in a resistor when a current 'I' flows through it for a time 't' is given by H = I²Rt (Joule's Law).
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