A circuit has two resistors in parallel, R1 = 4 ohms and R2 = 12 ohms, connected to a 9 V battery. Calculate the equivalent resistance, supply current, and current through each resistor.

Step 1: Identify the given values. Two resistors are connected in parallel: R_1 = 4 and R_2 = 12 . The battery voltage is V = 9 V. a) Determine the equivalent circuit resistance. For resistors connected in parallel, the equivalent resistance R_eq is given by the formula: (1)/(R_eq) = (1)/(R_1) + (1)/(R_2) Substitute the given values: (1)/(R_eq) = (1)/(4 ) + (1)/(12 ) Find a common denominator: (1)/(R_eq) = (3)/(12 ) + (1)/(12 ) (1)/(R_eq) = (3+1)/(12 ) (1)/(R_eq) = (4)/(12 ) (1)/(R_eq) = (1)/(3 ) Invert both sides to find R_eq: R_eq = 3 The equivalent circuit resistance is 3 . b) Determine the supply current. The supply current I_supply can be found using Ohm's Law, I = (V)/(R_eq), where V is the battery voltage and R_eq is the equivalent resistance of the parallel combination. I_supply = 9 V3 I_supply = 3 A The supply current is 3 A. c) Determine the current in each resistor. In a parallel circuit, the voltage across each resistor is the same as the supply voltage. For resistor R_1: I_1 = (V)/(R_1) = 9 V4 I_1 = 2.25 A For resistor R_2: I_2 = (V)/(R_2) = 9 V12 I_2 = 0.75 A The current in the 4 resistor is 2.25 A. The current in the 12 resistor is 0.75 A. That's 2 down. 3 left today — send the next one.