1. using kirchhoff’s rules, construct enough mathematically independent equations to solve for the current of each resistor. then calculate the % error between your measured and theoretical values for the current of each resistor. you must use both of kirchhoff’s rules (you must use at least 1 junction equation) and show work to receive any credi
To solve for the currents in a circuit using Kirchhoff's rules, we need to apply Kirchhoff's junction rule (also known as Kirchhoff's current law) and Kirchhoff's loop rule (also known as Kirchhoff's voltage law).
Let's consider a simple circuit with three resistors connected in series to a voltage source. We'll label the resistors as R1, R2, and R3, and the currents flowing through them as I1, I2, and I3, respectively.
Applying Kirchhoff's junction rule: At any junction or node in the circuit, the sum of the currents entering the node is equal to the sum of the currents leaving the node.
At the junction connecting the three resistors, we have: I1 = I2 + I3 -- Equation (1)
Applying Kirchhoff's loop rule: In any closed loop within the circuit, the sum of the potential differences (voltages) across the elements is equal to zero.
Let's consider the loop that includes R1, R2, and R3. Starting from a reference point, we traverse the loop in a clockwise direction. We can write the equation as follows:
V - I1 * R1 - I2 * R2 - I3 * R3 = 0 -- Equation (2)
These two equations (Equation 1 and Equation 2) are mathematically independent and can be solved simultaneously to determine the values of I1, I2, and I3.
To calculate the percent error between the measured and theoretical values, we need additional information, such as the resistance values (R1, R2, and R3) and the voltage (V) applied across the circuit. With this information, we can substitute the values into the equations and solve them. Then, by comparing the measured values of the currents with the theoretical values obtained from the equations, we can calculate the percent error using the following formula:
% Error = [(Theoretical Value - Measured Value) / Theoretical Value] * 100
Please provide the specific resistance values and the applied voltage to continue with the calculations and provide you with the percent error for each resistor.