Calculate the potential difference across a 10 resistor carrying current of 2 A.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here are the solutions to the problems:
Problem 1:
Calculate the potential difference across a 10 $\Omega$ resistor carrying current of 2 A.
Step 1: Identify the given values.
Resistance $R = 10 \Omega$
Current $I = 2 \text{ A}$
Step 2: Use Ohm's Law to calculate the potential difference $V$.
The formula for Ohm's Law is $V = IR$.
$$V = (2 \text{ A}) \times (10 \Omega)$$
$$V = 20 \text{ V}$$
$$\boxed{\text{Potential difference } V = 20 \text{ V}}$$
Problem 2:
The potential difference across a 3 $\Omega$ resistor is 12 V. What is the current flowing?
Step 1: Identify the given values.
Resistance $R = 3 \Omega$
Potential difference $V = 12 \text{ V}$
Step 2: Use Ohm's Law to calculate the current $I$.
Rearranging Ohm's Law $V = IR$ for $I$:
$$I = \frac{V}{R}$$
$$I = \frac{12 \text{ V}}{3 \Omega}$$
$$I = 4 \text{ A}$$
$$\boxed{\text{Current } I = 4 \text{ A}}$$
Problem 3:
Find the potential difference across a conductor of resistance 2 $\Omega$ if the charge of 180 C flows for 2 minutes.
Step 1: Identify the given values and convert units.
Resistance $R = 2 \Omega$
Charge $Q = 180 \text{ C}$
Time $t = 2 \text{ minutes} = 2 \times 60 \text{ s} = 120 \text{ s}$
Step 2: Calculate the current $I$ using the formula $I = \frac{Q}{t}$.
$$I = \frac{180 \text{ C}}{120 \text{ s}}$$
$$I = 1.5 \text{ A}$$
Step 3: Use Ohm's Law to calculate the potential difference $V$.
The formula for Ohm's Law is $V = IR$.
$$V = (1.5 \text{ A}) \times (2 \Omega)$$
$$V = 3 \text{ V}$$
$$\boxed{\text{Potential difference } V = 3 \text{ V}}$$
Problem 4:
A current of 4 A flows through an electric kettle. The p.d. across it is 8 V. Find the resistance.
Step 1: Identify the given values.
Current $I = 4 \text{ A}$
Potential difference $V = 8 \text{ V}$
Step 2: Use Ohm's Law to calculate the resistance $R$.
Rearranging Ohm's Law $V = IR$ for $R$:
$$R = \frac{V}{I}$$
$$R = \frac{8 \text{ V}}{4 \text{ A}}$$
$$R = 2 \Omega$$
$$\boxed{\text{Resistance } R = 2 \Omega}$$
Problem 5:
The potential difference across a 2 k$\Omega$ resistor is 4 V. Determine the current flowing in the circuit.
Step 1: Identify the given values and convert units.
Resistance $R = 2 \text{ k}\Omega = 2 \times 10^3 \Omega = 2000 \Omega$
Potential difference $V = 4 \text{ V}$
Step 2: Use Ohm's Law to calculate the current $I$.
Rearranging Ohm's Law $V = IR$ for $I$:
$$I = \frac{V}{R}$$
$$I = \frac{4 \text{ V}}{2000 \Omega}$$
$$I = 0.002 \text{ A}$$
This can also be expressed in milliamperes:
$$I = 2 \times 10^{-3} \text{ A} = 2 \text{ mA}$$
$$\boxed{\text{Current } I = 0.002 \text{ A (or } 2 \text{ mA)}}$$
