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To solve the given circuit numerically, we will: * Use **Kirchhoff’s Laws** (KVL and KCL). * Label the currents and loop directions. * Solve the resulting equations. ### Given: Resistances: * ( R_1 = 0.5,\Omega ) * ( R_2 = 1,\Omega ) * ( R_3 = 10,\Omega ) EMFs: * ( E_1 = 9,V ) (upper battery) * ( E_2 = 12,V ) (lower battery) Let’s assign: * Current ( I_1 ): through upper branch (9V battery + 0.5Ω) * Current ( I_2 ): through middle branch (12V battery + 1Ω) * Current ( I_3 ): through lower branch (10Ω resistor) Using **Kirchhoff’s Current Law (KCL)** at the left junction: [ I_3 = I_1 + __________ _______ _________ __________ _____ ________ __________ ________ _____.
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