Consider a star network as shown in the following figure : If the resistance between terminals b and c with a open is represented by RA, the resistance between c and a with b open is RB and the resistance between a and b with c open is RC, then arrange RA, RB and RC in descending order.
RA, RB, RC
To solve this problem, we need to calculate the effective resistance for each pair of terminals when the third terminal is open. Let's break down the problem:
- Resistance between terminals b and c with a open (RA):
When terminal a is open, the 2Ω resistor is disconnected from the circuit. Therefore, the effective resistance between b and c is simply the series combination of the 4Ω and 7Ω resistors.
\(R_A = 4\, \Omega + 7\, \Omega = 11\, \Omega\)
- Resistance between terminals c and a with b open (RB):
When terminal b is open, the 4Ω resistor is disconnected from the circuit. The effective resistance between c and a is just the series combination of the 2Ω and 7Ω resistors.
\(R_B = 2\, \Omega + 7\, \Omega = 9\, \Omega\)
- Resistance between terminals a and b with c open (RC):
When terminal c is open, the 7Ω resistor is disconnected from the circuit. The effective resistance between a and b is the series combination of the 2Ω and 4Ω resistors.
\(R_C = 2\, \Omega + 4\, \Omega = 6\, \Omega\)
Now, we can arrange the calculated resistances in descending order:
\(R_A = 11\, \Omega\), \(R_B = 9\, \Omega\), \(R_C = 6\, \Omega\)
Thus, the descending order is: RA, RB, RC.
The correct answer is: RA, RB, RC.
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