What power would be consumed by the series resistor in the circuit shown in the illustration if the source is 30 volts, the resistance for R1 is 10 ohms, R2 is 10 ohms and R3 is 10 ohms? Illustration EL-0032
• Carefully identify which resistor is the series resistor in diagram B when the switch is closed • Find the equivalent resistance of R1 and R2 in the parallel branch, then add the series resistor • Use power formulas: P = I^2 R and P = V × I
• In diagram B, which resistor has the same current as the source, and which resistors share the current? The one with the same current is the series resistor. • Once you replace the parallel pair with a single equivalent resistance, what is the total circuit resistance, and therefore the circuit current from a 30‑volt source? • After you find the current, how can you use it with the resistance of the series resistor alone to get the power it consumes?
• Be sure you combined R1 and R2 as parallel resistors: ( R_{eq} = \frac{R_1 R_2}{R_1 + R_2} ) • Confirm that the total resistance is series sum: ( R_T = R_3 + R_{eq} ) • Check that you used the current through the series resistor only when applying ( P = I^2 R ) or ( P = V I )
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