Consider the circuit in the diagram. Let R1 = 51.0 Ω, R2 = 38.0 Ω, R3 = 74.0 Ω, R4 = 16.0 Ω, and V = 84 V.
(b) What current flows from the battery?
(c) What is the potential difference between points A and B?
(d) What current flows through each branch between points A and B?
(e) Determine the power dissipated in the 51.0-Ω resistor, the 74.0-Ω resistor, and the 38.0-Ω resistor.
diagram?
To solve the given circuit problems, we need to understand the rules and laws of electrical circuits. In this case, Ohm's law and Kirchhoff's laws are applicable.
(a) To determine the current flowing from the battery, we can use Kirchhoff's current law (KCL) at point A. According to KCL, the current entering a junction is equal to the current leaving the junction.
At point A, the circuit branches into two paths: one including R1 and R3, and the other including R2 and R4. The sum of currents entering point A must be equal to the sum of currents leaving the point.
I_battery = I_R1 + I_R3 = I_R2 + I_R4
We can find the individual currents by using Ohm's law, which states that the current flowing through a resistor is equal to the voltage across it divided by its resistance.
I = V / R
Using this formula, we can calculate the currents through each resistor:
I_R1 = V / R1
I_R2 = V / R2
I_R3 = V / R3
I_R4 = V / R4
(b) To find the current flowing from the battery, we can sum the currents through R1 and R3 or R2 and R4:
I_battery = I_R1 + I_R3 (or) I_battery = I_R2 + I_R4
Substitute the given values for resistances and voltage into the equations and calculate the currents.
(c) The potential difference between points A and B can be found by calculating the voltage drop across resistor R1 or R3.
V_AB = I_R1 * R1 (or) V_AB = I_R3 * R3
Substitute the calculated current and resistance values to find the potential difference.
(d) To determine the current flowing through each branch between points A and B, we can use Ohm's law. The current in each branch is equal to the potential difference between points A and B divided by the resistance of the corresponding resistor.
I_branch1 = V_AB / R1
I_branch2 = V_AB / R3
(e) The power dissipated in a resistor can be calculated using the formula:
P = I^2 * R
Using the calculated currents and resistances, we can find the power dissipated in each resistor:
Power_R1 = I_R1^2 * R1
Power_R2 = I_R2^2 * R2
Power_R3 = I_R3^2 * R3
Substitute the calculated values into the formula to find the power dissipated in each resistor.