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The image provided is a diagram of a circuit with resistors and capacitors. To analyze the constraints, we need to consider the following:

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1. Resistor Values: The values of the resistors in the circuit are given as ( R_1 = 10 \Omega ), ( R_2 = 20 \Omega ), and ( R_3 = 30 \Omega ).

2. Capacitor Values: The values of the capacitors are given as ( C_1 = 5 \mu F ) and ( C_2 = 10 \mu F ).

3. Power Supply: The power supply voltage is ( V_s = 12V ).

4. Circuit Configuration: The circuit consists of three resistors (( R_1 ), ( R_2 ), and ( R_3 )) connected in series with two capacitors (( C_1 ) and ( C_2 )).

Constraints:

• Ohm's Law: The current through each resistor can be calculated using Ohm's Law, ( I = \frac{V}{R} ).
• Kirchhoff's Voltage Law (KVL): The sum of all voltages around any closed loop in the circuit must equal zero.
• Capacitance Formula: The charge on a capacitor is given by ( Q = CV ), where ( C ) is the capacitance and ( V ) is the voltage across the capacitor.

To find the constraints, we need to determine the equivalent resistance of the resistors and the total charge stored in the capacitors.

Steps:

1. Calculate Equivalent Resistance:

   • Since the resistors are in series, the equivalent resistance ( R{eq} ) is the sum of individual resistances: [ R{eq} = R_1 + R_2 + R_3 = 10\Omega + 20\Omega + 30\Omega = 60\Omega ]

2. Calculate Total Current:

   • Using Ohm's Law, the total current ( I ) through the circuit is: [ I = \frac{Vs}{R{eq}} = \frac{12V}{60\Omega} = 0.2A ]

3. Calculate Voltages Across Resistors:

   Using Ohm's Law for each resistor: [ V_1 = IR_1 = 0.2A \times 10\Omega = 2V ] [ V_2 = IR_2 = 0.2A \times 20\Omega = 4V ] [ V_3 = IR_3 = 0.2A \times 30\Omega = 6V ]

4. Calculate Charges on Capacitors:

   • For ( C_1 ): [ Q_1 = C_1 \times V_1 = 5\mu F \times 2V = 10\mu C ]
   • For ( C_2 ): [ Q_2 = C_2 \times V_2 = 10\mu F \times 4V = 40\mu C ]

Summary of Constraints:

• The equivalent resistance of the circuit is ( 60\Omega ).
• The total current flowing through the circuit is ( 0.2A ).
• The voltages across the resistors are ( 2V ), ( 4V ), and ( 6V ).
• The charges on the capacitors are ( 10\mu C ) and ( 40\mu C ).