Calculating the Equivalent Resistance of Parallel Resistors

When two resistors are connected in parallel, the equivalent resistance can be calculated using the following formula:

1/R_eq = 1/R_1 + 1/R_2

Where R_eq is the equivalent resistance, R_1 and R_2 are the values of the individual resistors.

Calculating the Percentage Error

To calculate the percentage error in the equivalent resistance, we need to first calculate the individual percentage errors for each resistor. This can be done using the following formula:

% error = (|measured value - true value| / true value) x 100%

Where measured value is the value obtained through measurement, true value is the actual value of the resistor, and | | represents absolute value.

Once we have the percentage errors for each resistor, we can calculate the total percentage error in the equivalent resistance using the following formula:

% error_eq = % error_1 + % error_2

Where % error_1 and % error_2 are the percentage errors for each individual resistor.

Using the Given Values

For the given resistors with values of (5±0.2) kiloohm and (10.0±0.1) kiloohm, we can calculate the individual percentage errors as follows:

% error_1 = (0.2 / 5) x 100% = 4%
% error_2 = (0.1 / 10.0) x 100% = 1%

Using the formula for equivalent resistance in parallel, we can calculate the equivalent resistance as follows:

1/R_eq = 1/5 + 1/10.0
R_eq = 3.33 kiloohm

Using the formula for total percentage error, we can calculate the percentage error in the equivalent resistance as follows:

% error_eq = 4% + 1% = 5%

Therefore, the percentage error in the equivalent resistance when the two resistors are connected in parallel is 5%.