1. **Stating the problem:** We have a circuit with three resistors R1, R2, and R3 each of 1000 Ω, and source voltages Vs of 5 V, 10 V, and 15 V. The measured voltages across each resistor (VR1, VR2, VR3) and currents through each resistor (Ir1, Ir2, Ir3) are given. We need to verify Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) for these values. 2. **Kirchhoff's Current Law (KCL):** KCL states that the sum of currents entering a node equals the sum of currents leaving the node. 3. **Kirchhoff's Voltage Law (KVL):** KVL states that the sum of voltages around any closed loop in a circuit is zero. 4. **Check KCL for each Vs:** - For Vs = 5 V: $$I_{r1} = 3.33\,mA,\quad I_{r2} = 1.67\,mA,\quad I_{r3} = 1.67\,mA$$ Sum of currents leaving node: $$I_{r2} + I_{r3} = 1.67 + 1.67 = 3.34\,mA$$ Compare with $$I_{r1} = 3.33\,mA$$ Difference: $$|3.33 - 3.34| = 0.01\,mA$$ (negligible, KCL holds) - For Vs = 10 V: $$I_{r1} = 6.67\,mA,\quad I_{r2} = 3.33\,mA,\quad I_{r3} = 3.33\,mA$$ Sum $$I_{r2} + I_{r3} = 6.66\,mA$$ Difference: $$|6.67 - 6.66| = 0.01\,mA$$ (negligible, KCL holds) - For Vs = 15 V: $$I_{r1} = 10.01\,mA,\quad I_{r2} = 5.0\,mA,\quad I_{r3} = 5.0\,mA$$ Sum $$I_{r2} + I_{r3} = 10.0\,mA$$ Difference: $$|10.01 - 10.0| = 0.01\,mA$$ (negligible, KCL holds) 5. **Check KVL for each Vs:** - For Vs = 5 V: Sum of voltages across resistors: $$V_{R1} + V_{R2} + V_{R3} = 3.333 + 1.66 + 1.66 = 6.653\,V$$ This is slightly higher than Vs (5 V), likely due to measurement or rounding errors. - For Vs = 10 V: Sum: $$6.667 + 3.38 + 3.38 = 13.427\,V$$ Vs is 10 V, discrepancy again likely due to rounding. - For Vs = 15 V: Sum: $$10.1 + 5.1 + 5.1 = 20.3\,V$$ Vs is 15 V, discrepancy noted. 6. **Explanation:** KCL is well satisfied within small measurement errors. KVL sums exceed Vs, indicating possible measurement or data inconsistency. **Final conclusion:** - KCL holds well for all cases. - KVL shows discrepancies likely due to measurement errors.