Question

1. the probable fault in this circuit is

a r1 shorted
b r2 shorted
c c1 shorted
d c2 shorted

Explanation:

1. Analyze R1: The voltage across R1 is 9.93 V, and its resistance is 1 kΩ. Using Ohm's Law ($I = \frac{V}{R}$), the current is $\frac{9.93\ V}{1\ k\Omega} = 9.93\ mA$, which matches the predicted current. So R1 is not shorted (if R1 were shorted, voltage across it would be 0, current would be different).
2. Analyze R2: The voltage across R2 is 10 V, resistance 1 kΩ, current $\frac{10\ V}{1\ k\Omega} = 10\ mA$, but predicted current is 4.02 mA. However, if C1 is shorted, it would affect the circuit.
3. Analyze C1: Capacitors at AC (70 kHz) act as low impedance, but a shorted capacitor (C1 shorted) would make the voltage across R1 close to the source voltage (since C1 is shorted, it's like a wire). The voltage across R1 is 9.93 V (close to 10 V), and current is 9.93 mA (matches $\frac{9.93\ V}{1\ k\Omega}$). For R2's branch, if C1 is shorted, the AC signal path is altered, but the key is R1's voltage. If C1 were not shorted, at 70 kHz, a 0.02 μF capacitor has reactance $X_{C1}=\frac{1}{2\pi f C}=\frac{1}{2\pi\times70\times10^3\times0.02\times10^{-6}}\approx113\ \Omega$, so R1 (1 kΩ) and $X_{C1}$ would divide the voltage, but here R1 has ~10 V, implying C1 is shorted (acts as 0 impedance, so all voltage across R1).
4. C2 shorted: Would affect R2's branch, but R2 has 10 V, which doesn't fit a shorted C2 (C2 shorted would make R2's voltage related to AC, but here R2 has DC-like 10 V? No, the source is AC, but the voltage across R2 is 10 V, same as source. If C1 is shorted, the top branch has R1 with ~10 V, and the bottom branch: if C1 is shorted, the AC signal to R2's branch is affected, but the main clue is R1's voltage. So C1 shorted explains R1's voltage and current, while R2's current discrepancy is due to C1 shorting affecting the circuit's AC path (but the key fault is C1 shorted as R1's voltage/current match when C1 is shorted, and R1 isn't shorted, R2's issue is secondary to C1's fault).

Answer:

c. C1 shorted